JEE Main & Advanced Mathematics Probability Question Bank

done Definition of probability Total Questions - 153

• question_answer1)
  Two card are drawn successively with replacement from a pack of 52 cards. The probability of drawing two aces is [MNR 1988; UPSEAT 2000]
  A)
                              \[\frac{1}{169}\]   done clear
  B)
                  \[\frac{1}{221}\] done clear
  C)
                  \[\frac{1}{2652}\] done clear
  D)
                  \[\frac{4}{663}\] done clear
  View Solution play_arrow

• question_answer2)
  In a single throw of two dice, the probability of getting more than 7 is                                           [MP PET 1991]
  A)
                  \[\frac{7}{36}\]     done clear
  B)
                  \[\frac{7}{12}\] done clear
  C)
                  \[\frac{5}{12}\]     done clear
  D)
                  \[\frac{5}{36}\] done clear
  View Solution play_arrow

• question_answer3)
  The probability of drawing a white ball from a bag containing 3 black balls and 4 white balls, is
  A)
                  \[\frac{4}{7}\]        done clear
  B)
                  \[\frac{3}{7}\] done clear
  C)
                  \[\frac{1}{7}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer4)
  A and B toss a coin alternatively, the first to show a head being the winner. If A starts the game, the chance of his winning is                                              [MP PET 1987]
  A)
                  5/8          done clear
  B)
                  1/2 done clear
  C)
                  1/3          done clear
  D)
                  2/3 done clear
  View Solution play_arrow

• question_answer5)
  If two balanced dice are tossed once, the probability of the event,  that the sum of the integers coming on the upper sides of the two dice is 9, is                                         [MP PET 1987]
  A)
                  \[\frac{7}{18}\]     done clear
  B)
                  \[\frac{5}{36}\] done clear
  C)
                  \[\frac{1}{9}\]        done clear
  D)
                  \[\frac{1}{6}\] done clear
  View Solution play_arrow

• question_answer6)
  From a well shuffled pack of cards one card is drawn at random. The probability that the card drawn is an ace is
  A)
                  \[\frac{1}{13}\]     done clear
  B)
                  \[\frac{4}{13}\] done clear
  C)
                  \[\frac{3}{52}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer7)
  A single letter is selected at random from the word ?PROBABILITY?. The probability that the selected letter is a vowel is     [MNR 1986; UPSEAT 2000]
  A)
                  \[\frac{2}{11}\]     done clear
  B)
                  \[\frac{3}{11}\] done clear
  C)
                  \[\frac{4}{11}\]     done clear
  D)
                  0 done clear
  View Solution play_arrow

• question_answer8)
  There are n letters and n addressed envelopes. The probability that all the letters are not kept in the right envelope, is
  A)
                  \[\frac{1}{n\,!}\]     done clear
  B)
                  \[1-\frac{1}{n\,!}\] done clear
  C)
                  \[1-\frac{1}{n}\]    done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer9)
  From a book containing 100 pages, one page is selected randomly. The probability that the sum of the digits of the page number of the selected page is 11, is
  A)
                  \[\frac{2}{25}\]     done clear
  B)
                  \[\frac{9}{100}\] done clear
  C)
                  \[\frac{11}{100}\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer10)
  There are two childrens in a family. The probability that both of them are boys is
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{1}{3}\] done clear
  C)
                  \[\frac{1}{4}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer11)
  If a dice is thrown twice, then the probability of getting 1 in the first throw only is
  A)
                  \[\frac{1}{36}\]     done clear
  B)
                  \[\frac{3}{36}\] done clear
  C)
                  \[\frac{5}{36}\]     done clear
  D)
                  \[\frac{1}{6}\] done clear
  View Solution play_arrow

• question_answer12)
  Two cards are drawn one by one at random from a pack of 52 cards. The probability that both of them are king, is [MP PET 1994]
  A)
                  \[\frac{2}{13}\]     done clear
  B)
                  \[\frac{1}{169}\] done clear
  C)
                  \[\frac{1}{221}\]   done clear
  D)
                  \[\frac{30}{221}\] done clear
  View Solution play_arrow

• question_answer13)
  A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows 6 is [MP PET 1994; Pb. CET 2001]
  A)
                  \[\frac{1}{8}\]        done clear
  B)
                  \[\frac{1}{12}\] done clear
  C)
                  \[\frac{1}{2}\]        done clear
  D)
                  1 done clear
  View Solution play_arrow

• question_answer14)
  A coin is tossed twice. The probability of getting head both the  times is                                      [MNR 1978]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{1}{4}\] done clear
  C)
                  \[\frac{3}{4}\]        done clear
  D)
                  1 done clear
  View Solution play_arrow

• question_answer15)
  From a pack of 52 cards two are drawn with replacement. The probability, that the first is a diamond and the second is a king, is                                      [MNR 1979]
  A)
                  \[\frac{1}{26}\]     done clear
  B)
                  \[\frac{17}{2704}\] done clear
  C)
                  \[\frac{1}{52}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer16)
  Two dice are thrown simultaneously. The probability of getting the sum 2 or 8 or 12 is
  A)
                  \[\frac{5}{18}\]     done clear
  B)
                  \[\frac{7}{36}\] done clear
  C)
                  \[\frac{7}{18}\]     done clear
  D)
                  \[\frac{5}{36}\] done clear
  View Solution play_arrow

• question_answer17)
  A dice is thrown twice. The probability of getting 4, 5 or 6 in the first throw and 1, 2, 3 or 4 in the second throw is
  A)
                  1              done clear
  B)
                  \[\frac{1}{3}\] done clear
  C)
                  \[\frac{7}{36}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer18)
  Two cards are drawn from a pack of 52 cards. What is the probability that at least one of the cards drawn is an ace
  A)
                  \[\frac{33}{221}\] done clear
  B)
                  \[\frac{188}{221}\] done clear
  C)
                  \[\frac{1}{26}\]     done clear
  D)
                  \[\frac{21}{221}\] done clear
  View Solution play_arrow

• question_answer19)
  One card is drawn from each of two ordinary packs of 52 cards. The probability that at least one of them is an ace of heart, is
  A)
                  \[\frac{103}{2704}\]            done clear
  B)
                  \[\frac{1}{2704}\] done clear
  C)
                  \[\frac{2}{52}\]     done clear
  D)
                  \[\frac{2601}{2704}\] done clear
  View Solution play_arrow

• question_answer20)
  A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is rusted or is a nail [MP PET 1992, 2000]
  A)
                  \[\frac{3}{16}\]     done clear
  B)
                  \[\frac{5}{16}\] done clear
  C)
                  \[\frac{11}{16}\]   done clear
  D)
                  \[\frac{14}{16}\] done clear
  View Solution play_arrow

• question_answer21)
  The probability of getting at least one tail in 4 throws of a coin is   [MNR 1983; Kurukshetra CEE 1998]
  A)
                  \[\frac{15}{16}\]   done clear
  B)
                  \[\frac{1}{16}\] done clear
  C)
                  \[\frac{1}{4}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer22)
  Three letters are to be sent to different persons and addresses on the three envelopes are also written. Without looking at the addresses, the probability that the letters go into the right envelope is equal to [MNR 1982; MP PET 1990; Orissa JEE 2004]
  A)
                  \[\frac{1}{27}\]     done clear
  B)
                  \[\frac{1}{9}\] done clear
  C)
                  \[\frac{4}{27}\]     done clear
  D)
                  \[\frac{1}{6}\] done clear
  View Solution play_arrow

• question_answer23)
  Two dice are thrown. The probability that the sum of numbers appearing is more than 10, is
  A)
                  \[\frac{1}{18}\]     done clear
  B)
                  \[\frac{1}{12}\] done clear
  C)
                  \[\frac{1}{6}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer24)
  The probability of getting a total of 5 or 6 in a single throw of 2 dice is                                         [MP PET 1988]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{1}{4}\] done clear
  C)
                  \[\frac{1}{3}\]        done clear
  D)
                  \[\frac{1}{6}\] done clear
  View Solution play_arrow

• question_answer25)
  The probability of a sure event is                        [MP PET 1988]
  A)
                  0              done clear
  B)
                  1 done clear
  C)
                  2              done clear
  D)
                  \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer26)
  The probability of happening an event A in one trial is 0.4. The probability that  the event A happens at least once in three independent trials is [IIT 1980; Kurukshetra CEE 1998; DCE 2001]
  A)
                  0.936      done clear
  B)
                  0.784 done clear
  C)
                  0.904      done clear
  D)
                  0.216 done clear
  View Solution play_arrow

• question_answer27)
  In a single throw of two dice the probability of obtaining an odd number is
  A)
                  \[\frac{1}{6}\]        done clear
  B)
                  \[\frac{1}{2}\] done clear
  C)
                  \[\frac{1}{3}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer28)
  From 10,000 lottery tickets numbered from 1 to 10,000, one ticket is drawn at random. What is the probability that the number marked on the drawn ticket is divisible by 20
  A)
                  \[\frac{1}{100}\]   done clear
  B)
                  \[\frac{1}{50}\] done clear
  C)
                  \[\frac{1}{20}\]     done clear
  D)
                  \[\frac{1}{10}\] done clear
  View Solution play_arrow

• question_answer29)
  Two dice are thrown simultaneously. What is the probability of obtaining a multiple of 2 on one of them and a multiple of 3 on the other                                                [AI CBSE 1981]
  A)
                  \[\frac{5}{36}\]     done clear
  B)
                  \[\frac{11}{36}\] done clear
  C)
                  \[\frac{1}{6}\]        done clear
  D)
                  \[\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer30)
  A problem of mathematics is given to three students whose chances of solving the problem are 1/3, 1/4 and 1/5 respectively. The probability that the question will be solved is                                            [BIT Ranchi 1991; MP PET 1990]
  A)
                  \[\frac{2}{3}\]        done clear
  B)
                  \[\frac{3}{4}\] done clear
  C)
                  \[\frac{4}{5}\]        done clear
  D)
                  \[\frac{3}{5}\] done clear
  View Solution play_arrow

• question_answer31)
  The probability of getting number 5 in throwing a dice is [MP PET 1988]
  A)
                  1              done clear
  B)
                  \[\frac{1}{3}\] done clear
  C)
                  \[\frac{1}{6}\]        done clear
  D)
                  \[\frac{5}{6}\] done clear
  View Solution play_arrow

• question_answer32)
  A card is drawn from a well shuffled pack of cards. The probability of getting a queen of club or king of heart is [MP PET 1988]
  A)
                  \[\frac{1}{52}\]     done clear
  B)
                  \[\frac{1}{26}\] done clear
  C)
                  \[\frac{1}{18}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer33)
  In a simultaneous throw of three coins, what is the probability of getting at least 2 tails
  A)
                  \[\frac{1}{8}\]        done clear
  B)
                  \[\frac{1}{4}\] done clear
  C)
                  \[\frac{1}{2}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer34)
  In a throw of a die, what is the probability of getting a number less than 7
  A)
                  0              done clear
  B)
                  1 done clear
  C)
                  \[\frac{1}{2}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer35)
  Two dice are thrown simultaneously. What is the probability of obtaining sum of the numbers less than 11
  A)
                  \[\frac{17}{18}\]   done clear
  B)
                  \[\frac{1}{12}\] done clear
  C)
                  \[\frac{11}{12}\]   done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer36)
  The probability that an ordinary or a non-leap year has 53 sunday, is                                          [MP PET 1996]
  A)
                  \[\frac{2}{7}\]        done clear
  B)
                  \[\frac{1}{7}\] done clear
  C)
                  \[\frac{3}{7}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer37)
  A card is drawn at random from a pack of 52 cards. The probability that the drawn card is a court card i.e. a jack, a queen or a king, is
  A)
                  \[\frac{3}{52}\]     done clear
  B)
                  \[\frac{3}{13}\] done clear
  C)
                  \[\frac{4}{13}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer38)
  Two dice are thrown together. The probability that sum of the two numbers will be a multiple of 4 is      [MP PET 1990]
  A)
                  \[\frac{1}{9}\]        done clear
  B)
                  \[\frac{1}{3}\] done clear
  C)
                  \[\frac{1}{4}\]        done clear
  D)
                  \[\frac{5}{9}\] done clear
  View Solution play_arrow

• question_answer39)
  If in a lottary there are 5 prizes and 20 blanks, then the probability of getting a prize is
  A)
                  \[\frac{1}{5}\]        done clear
  B)
                  \[\frac{2}{5}\] done clear
  C)
                  \[\frac{4}{5}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer40)
  The probability of getting a number greater than 2 in throwing a die is                                         [MP PET 1988]
  A)
                  \[\frac{1}{3}\]        done clear
  B)
                  \[\frac{2}{3}\] done clear
  C)
                  \[\frac{1}{2}\]        done clear
  D)
                  \[\frac{1}{6}\] done clear
  View Solution play_arrow

• question_answer41)
  Two cards are drawn from a pack of 52 cards. What is the probability that one of them is a queen and the other is an ace
  A)
                  \[\frac{2}{663}\]   done clear
  B)
                  \[\frac{2}{13}\] done clear
  C)
                  \[\frac{4}{663}\]   done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer42)
  Two dice are thrown together. If the numbers appearing on the two dice are different, then what is the probability that the sum is 6
  A)
                  \[\frac{5}{36}\]     done clear
  B)
                  \[\frac{1}{6}\] done clear
  C)
                  \[\frac{2}{15}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer43)
  A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is 1/4 and that of the woman's selection is 1/3. What is the probability that none of them will be selected [MNR 1988]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{1}{12}\] done clear
  C)
                  \[\frac{1}{4}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer44)
  Three fair coins are tossed. If both heads and tails appears, then the probability that exactly one head appears, is
  A)
                  \[\frac{3}{8}\]        done clear
  B)
                  \[\frac{1}{6}\] done clear
  C)
                  \[\frac{1}{2}\]        done clear
  D)
                  \[\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer45)
  A bag contains 4 white, 5 black and 6 red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red
  A)
                  \[\frac{4}{15}\]     done clear
  B)
                  \[\frac{1}{2}\] done clear
  C)
                  \[\frac{2}{5}\]        done clear
  D)
                  \[\frac{2}{3}\] done clear
  View Solution play_arrow

• question_answer46)
  A card is drawn at random from a pack of cards. What is the probability that the drawn card is neither a heart nor a king
  A)
                  \[\frac{4}{13}\]     done clear
  B)
                  \[\frac{9}{13}\] done clear
  C)
                  \[\frac{1}{4}\]        done clear
  D)
                  \[\frac{13}{26}\] done clear
  View Solution play_arrow

• question_answer47)
  In a single throw of two dice what is the probability of getting a total 13
  A)
                  0              done clear
  B)
                  1 done clear
  C)
                  \[\frac{13}{36}\]   done clear
  D)
                  \[\frac{25}{36}\] done clear
  View Solution play_arrow

• question_answer48)
  Three dice are thrown simultaneously. What is the probability of obtaining a total of 17 or 18 [AI CBSE 1983]
  A)
                  \[\frac{1}{9}\]        done clear
  B)
                  \[\frac{1}{72}\] done clear
  C)
                  \[\frac{1}{54}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer49)
  A box contains 10 good articles and 6 with defects. One article is chosen at random. What is the probability that it is either good or has a defect [MP PET 1992, 2000]
  A)
                  \[\frac{24}{64}\]   done clear
  B)
                  \[\frac{40}{64}\] done clear
  C)
                  \[\frac{49}{64}\]   done clear
  D)
                  \[\frac{64}{64}\] done clear
  View Solution play_arrow

• question_answer50)
  The probability of happening of an impossible event i.e. \[P\,(\varphi )\] is                          [MP PET 1993]
  A)
                  1              done clear
  B)
                  0 done clear
  C)
                  2              done clear
  D)
                  ?1 done clear
  View Solution play_arrow

• question_answer51)
  A coin is tossed until a head appears or until the coin has been tossed five times. If a head does not occur on the first two tosses, then the probability that the coin will be tossed 5 times is                                              [CEE 1993]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{3}{5}\] done clear
  C)
                  \[\frac{1}{4}\]        done clear
  D)
                  \[\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer52)
  Two dice are tossed. The probability that the total score is a prime number is                                              [CEE 1993]
  A)
                  \[\frac{1}{6}\]        done clear
  B)
                  \[\frac{5}{12}\] done clear
  C)
                  \[\frac{1}{2}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer53)
  Three persons work independently on a problem. If the respective probabilities that they will solve it are 1/3, 1/4 and 1/5, then the probability that none can solve it [MNR 1990; UPSEAT 2000]
  A)
                  \[\frac{2}{5}\]        done clear
  B)
                  \[\frac{3}{5}\] done clear
  C)
                  \[\frac{1}{3}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer54)
  Two dice are thrown. The probability that the sum of the points on two dice will be 7, is           [IIT 1974; MNR 1981, 91; RPET 1995, 97, 2002; UPSEAT 2000]
  A)
                  \[\frac{5}{36}\]     done clear
  B)
                  \[\frac{6}{36}\] done clear
  C)
                  \[\frac{7}{36}\]     done clear
  D)
                  \[\frac{8}{36}\] done clear
  View Solution play_arrow

• question_answer55)
  The probability that an event will fail to happen is 0.05. The probability that the event will take place on 4 consecutive occasions is                                 [Roorkee 1990]
  A)
                  0.00000625          done clear
  B)
                  0.18543125 done clear
  C)
                  0.00001875          done clear
  D)
                  0.81450625 done clear
  View Solution play_arrow

• question_answer56)
  The chance of throwing at least 9 in a single throw with two dice, is                                              [SCRA 1980]
  A)
                  \[\frac{1}{18}\]     done clear
  B)
                  \[\frac{5}{18}\] done clear
  C)
                  \[\frac{7}{18}\]     done clear
  D)
                  \[\frac{11}{18}\] done clear
  View Solution play_arrow

• question_answer57)
  From the word `POSSESSIVE', a letter is chosen at random. The probability of it to be S is                      [SCRA 1987]
  A)
                  \[\frac{3}{10}\]     done clear
  B)
                  \[\frac{4}{10}\] done clear
  C)
                  \[\frac{3}{6}\]        done clear
  D)
                  \[\frac{4}{6}\] done clear
  View Solution play_arrow

• question_answer58)
  Three identical dice are rolled. The probability that same number will appear on each of them will be    [SCRA 1991;             MP PET 1989; IIT 1984; RPET 2000, 02; DCE 2001]
  A)
                  \[\frac{1}{6}\]        done clear
  B)
                  \[\frac{1}{36}\] done clear
  C)
                  \[\frac{1}{18}\]     done clear
  D)
                  \[\frac{3}{28}\] done clear
  View Solution play_arrow

• question_answer59)
  For the two events A and B, \[P(A)=0.38,\,\] \[P(B)=0.41,\] then the value of \[P(A\]not) is
  A)
                  0.41        done clear
  B)
                  0.62 done clear
  C)
                  0.59        done clear
  D)
                  0.21 done clear
  View Solution play_arrow

• question_answer60)
  The probabilities of winning the race by two athletes A and B are \[\frac{1}{5}\]and \[\frac{1}{4}.\] The probability of winning by neither of them, is
  A)
                  \[\frac{3}{5}\]        done clear
  B)
                  \[\frac{3}{4}\] done clear
  C)
                  \[\frac{2}{5}\]        done clear
  D)
                  \[\frac{4}{5}\] done clear
  View Solution play_arrow

• question_answer61)
  The probability  of getting head and tail alternately in three throws of a coin (or a throw of three coins), is              [RPET 1997]
  A)
                  \[\frac{1}{8}\]        done clear
  B)
                  \[\frac{1}{4}\] done clear
  C)
                  \[\frac{1}{3}\]        done clear
  D)
                  \[\frac{3}{8}\] done clear
  View Solution play_arrow

• question_answer62)
  If A and B are mutually exclusive events, then the value of P (A or B) is
  A)
                  0              done clear
  B)
                  ?1 done clear
  C)
                  1              done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer63)
  If A is a sure event, then the value of P (A not ) is
  A)
                  0              done clear
  B)
                  ?1 done clear
  C)
                  1              done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer64)
  A number is chosen at random from first ten natural numbers. The probability that number is odd and perfect square is
  A)
                  \[\frac{2}{9}\]        done clear
  B)
                  \[\frac{2}{5}\] done clear
  C)
                  \[\frac{3}{7}\]        done clear
  D)
                  \[\frac{1}{5}\] done clear
  View Solution play_arrow

• question_answer65)
  . A number is chosen from first 100 natural numbers. The probability that the number is even or divisible by 5, is
  A)
                  \[\frac{3}{4}\]        done clear
  B)
                  \[\frac{2}{3}\] done clear
  C)
                  \[\frac{4}{5}\]        done clear
  D)
                  \[\frac{3}{5}\] done clear
  View Solution play_arrow

• question_answer66)
  Two dice are thrown. If first shows 5, then the probability that the sum of the numbers appears on both is 8 or more than 8, is
  A)
                  \[\frac{1}{12}\]     done clear
  B)
                  \[\frac{11}{12}\] done clear
  C)
                  \[\frac{1}{3}\]        done clear
  D)
                  \[\frac{2}{3}\] done clear
  View Solution play_arrow

• question_answer67)
  A card is drawn randomly from a pack of playing cards. Then the probability that it is neither ace nor king, is
  A)
                  \[\frac{11}{13}\]   done clear
  B)
                  \[\frac{8}{13}\] done clear
  C)
                  \[\frac{10}{13}\]   done clear
  D)
                  \[\frac{12}{13}\] done clear
  View Solution play_arrow

• question_answer68)
  There are 4 envelopes with addresses and 4 concerning letters. The probability that letter does not go into concerning proper envelope, is or There are four letters and four addressed envelopes. The chance that all letters are not despatched in the right envelope is             [RPET 1997; MP PET 1999; DCE 1999]
  A)
                  \[\frac{19}{24}\]   done clear
  B)
                  \[\frac{21}{23}\] done clear
  C)
                  \[\frac{23}{24}\]   done clear
  D)
                  \[\frac{1}{24}\] done clear
  View Solution play_arrow

• question_answer69)
  There are n letters and n addressed envelops. The probability that each letter takes place in right envelop is
  A)
                  \[\frac{1}{n\,!}\]     done clear
  B)
                  \[\frac{1}{(n-1)\,!}\] done clear
  C)
                  \[1-\frac{1}{n\,!}\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer70)
  If the probabilities of boy and girl to be born are same, then in a 4 children family the probability of being at least one girl, is
  A)
                  \[\frac{14}{16}\]   done clear
  B)
                  \[\frac{15}{16}\] done clear
  C)
                  \[\frac{1}{8}\]        done clear
  D)
                  \[\frac{3}{8}\] done clear
  View Solution play_arrow

• question_answer71)
  A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non-zero is
  A)
                  \[\frac{3}{16}\]     done clear
  B)
                  \[\frac{3}{8}\] done clear
  C)
                  \[\frac{1}{4}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer72)
  The event A is independent of itself if and only if \[P(A)=\]
  A)
                  0              done clear
  B)
                  1 done clear
  C)
                  0, 1         done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer73)
  A locker can be opened by dialing a fixed three digit code (between 000 and 999). A stranger who does not know the code tries to open the locker by dialing three digits at random. The probability that the stranger succeeds at the \[{{k}^{th}}\]trial is
  A)
                  \[\frac{k}{999}\]   done clear
  B)
                  \[\frac{k}{1000}\] done clear
  C)
                  \[\frac{k-1}{1000}\]             done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer74)
  In a throw of three dice, the probability that at least one die shows up 1, is                                  [DSSE 1981]
  A)
                  \[\frac{5}{6}\]        done clear
  B)
                  \[\frac{91}{216}\] done clear
  C)
                  \[\frac{1}{36}\]     done clear
  D)
                  \[\frac{125}{216}\] done clear
  View Solution play_arrow

• question_answer75)
  A card is drawn at random from a well shuffled pack of 52 cards. The probability of getting a two of heart or diamond is                                                     [DSSE 1979]
  A)
                  \[\frac{1}{26}\]     done clear
  B)
                  \[\frac{1}{52}\] done clear
  C)
                  \[\frac{1}{13}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer76)
  A man and his wife appear for an interview for two posts. The probability of the husband's selection is \[\frac{1}{7}\] and that of the wife's selection is \[\frac{1}{5}\]. What is the probability that only one of them will be selected [AISSE 1987; DSSE 1979, 81, 84]
  A)
                  \[\frac{1}{7}\]        done clear
  B)
                  \[\frac{2}{7}\] done clear
  C)
                  \[\frac{3}{7}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer77)
  A bag contains 5 white, 7 red and 8 black balls. If four balls are drawn one by one without replacement, what is the probability that all are white                                       [AISSE 1987]
  A)
                  \[\frac{1}{969}\]   done clear
  B)
                  \[\frac{1}{380}\] done clear
  C)
                  \[\frac{5}{20}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer78)
  The probability of A, B, C solving a problem are \[\frac{1}{3},\,\frac{2}{7},\,\frac{3}{8}\]respectively. If all the three try to solve the problem simultaneously, the probability that exactly one of them will solve it, is                                         [DSSE 1987]
  A)
                  \[\frac{25}{168}\] done clear
  B)
                  \[\frac{25}{56}\] done clear
  C)
                  \[\frac{20}{168}\] done clear
  D)
                  \[\frac{30}{168}\] done clear
  View Solution play_arrow

• question_answer79)
  In a single throw of two dice, the probability of obtaining a total of 7 or 9, is                                                [AISSE 1979]
  A)
                  \[\frac{5}{18}\]     done clear
  B)
                  \[\frac{1}{6}\] done clear
  C)
                  \[\frac{1}{9}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer80)
  A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another ticket is drawn without replacement. The probability that both the tickets will show even number, is                                                 [AI CBSE 1986]
  A)
                  \[\frac{9}{19}\]     done clear
  B)
                  \[\frac{8}{18}\] done clear
  C)
                  \[\frac{9}{18}\]     done clear
  D)
                  \[\frac{4}{19}\] done clear
  View Solution play_arrow

• question_answer81)
  The probability of hitting a target by three marksmen are \[\frac{1}{2},\,\frac{1}{3}\] and \[\frac{1}{4}\] respectively. The probability that one and only one of them will hit the target when they fire simultaneously, is                                             [AI CBSE 1982]
  A)
                  \[\frac{11}{24}\]   done clear
  B)
                  \[\frac{1}{12}\] done clear
  C)
                  \[\frac{1}{8}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer82)
  A determinant is chosen at random. The set of all determinants of order 2 with elements 0 or 1 only. The probability that value of the determinant chosen is positive, is                                                       [IIT 1982]
  A)
                  3/16        done clear
  B)
                  3/8 done clear
  C)
                  1/4          done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer83)
  One card is drawn from a pack of 52 cards. The probability that it is a king or diamond is [MP PET 1990, 1994; RPET 1996]
  A)
                  \[\frac{1}{26}\]     done clear
  B)
                  \[\frac{3}{26}\] done clear
  C)
                  \[\frac{4}{13}\]     done clear
  D)
                  \[\frac{3}{13}\] done clear
  View Solution play_arrow

• question_answer84)
  A bag contains 3 white, 3 black and 2 red balls. One by one three balls are drawn without replacing them. The probability that the third ball is red, is [MNR 1994]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{1}{3}\] done clear
  C)
                  \[\frac{2}{3}\]        done clear
  D)
                  \[\frac{1}{4}\] done clear
  View Solution play_arrow

• question_answer85)
  The probability of obtaining sum ?8? in a single throw of two dice                                                 [RPET 1995]
  A)
    \[\frac{1}{36}\]   done clear
  B)
    \[\frac{5}{36}\] done clear
  C)
                  \[\frac{4}{36}\]     done clear
  D)
                  \[\frac{6}{36}\] done clear
  View Solution play_arrow

• question_answer86)
  For any event A                                     [RPET 1995]
  A)
                  \[P(A)+P(\bar{A})=0\]        done clear
  B)
                  \[P(A)+P(\bar{A})=1\] done clear
  C)
                  \[P(A)>1\]              done clear
  D)
                  \[P(\bar{A})<1\] done clear
  View Solution play_arrow

• question_answer87)
  A box contains 3 white and 2 red balls. A ball is drawn and another ball is drawn without replacing first ball, then the probability of second ball to be red is      [Roorkee 1995]
  A)
                  \[\frac{8}{25}\]     done clear
  B)
                  \[\frac{2}{5}\] done clear
  C)
                  \[\frac{3}{5}\]        done clear
  D)
                  \[\frac{21}{25}\] done clear
  View Solution play_arrow

• question_answer88)
  The probability of India winning a test match against West Indies is \[\frac{1}{2}\]. Assuming independence from match to match, the probability that in a 5 match series India's second win occurs at the third test, is          [IIT 1995; Pb. CET 2003]
  A)
                  \[\frac{2}{3}\]        done clear
  B)
                  \[\frac{1}{2}\] done clear
  C)
                  \[\frac{1}{4}\]        done clear
  D)
                  \[\frac{1}{8}\] done clear
  View Solution play_arrow

• question_answer89)
  A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number which is a square is                                 [EAMCET 1989]
  A)
                  \[\frac{1}{5}\]        done clear
  B)
                  \[\frac{2}{5}\] done clear
  C)
                  \[\frac{1}{10}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer90)
  Seven chits are numbered 1 to 7. Three are drawn one by one with replacement. The probability that the least number on any selected chit is 5, is     [EAMCET 1991]
  A)
                  \[1-{{\left( \frac{2}{7} \right)}^{4}}\]              done clear
  B)
                  \[4\,{{\left( \frac{2}{7} \right)}^{4}}\] done clear
  C)
                  \[{{\left( \frac{3}{7} \right)}^{3}}\]  done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer91)
  If \[P(A)=0.65,\,\,P(B)=0.15,\] then \[P(\bar{A})+P(\bar{B})=\] [Pb. CET 1989; EAMCET 1988]
  A)
                  1.5          done clear
  B)
                  1.2 done clear
  C)
                  0.8          done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer92)
  For any two independent events \[{{E}_{1}}\] and \[{{E}_{2}},\] \[P\,\{({{E}_{1}}\cup {{E}_{2}})\cap ({{\bar{E}}_{1}}\cap {{\bar{E}}_{2}})\}\] is                                        [IIT 1991; Pb. CET 2003]
  A)
                  \[<\frac{1}{4}\]    done clear
  B)
                  \[>\frac{1}{4}\] done clear
  C)
                  \[\ge \frac{1}{2}\]  done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer93)
  For independent events \[{{A}_{1}},\,{{A}_{2}},\,..........,{{A}_{n}},\]  \[P({{A}_{i}})=\frac{1}{i+1},\]\[i=1,\,\,2,\,......,\,\,n.\] Then the probability that none of the event will occur, is
  A)
                  \[\frac{n}{n+1}\]  done clear
  B)
                  \[\frac{n-1}{n+1}\] done clear
  C)
                  \[\frac{1}{n+1}\]  done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer94)
  In order to get at least once a head with probability \[\ge 0.9,\] the number of times a coin needs to be tossed is                 [Roorkee 1989]
  A)
                  3              done clear
  B)
                  4 done clear
  C)
                  5              done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer95)
  A bag contains 3 black and 4 white balls. Two balls are drawn one by one at random without replacement. The probability that the second drawn ball is white, is [MP PET 1995]
  A)
                  \[\frac{4}{49}\]     done clear
  B)
                  \[\frac{1}{7}\] done clear
  C)
                  \[\frac{4}{7}\]        done clear
  D)
                  \[\frac{12}{49}\] done clear
  View Solution play_arrow

• question_answer96)
  ?A? draws two cards with replacement from a pack of 52 cards and ?B' throws a pair of dice what is the chance that ?A? gets both cards of same suit and ?B? gets total of 6 [MNR 1989]
  A)
                  \[\frac{1}{144}\]   done clear
  B)
                  \[\frac{1}{4}\] done clear
  C)
                  \[\frac{5}{144}\]   done clear
  D)
                  \[\frac{7}{144}\] done clear
  View Solution play_arrow

• question_answer97)
  A box contains 2 black, 4 white and 3 red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box, another ball is drawn at random and kept aside the first. This process is repeated till all the balls are drawn from the box. The probability that the balls drawn are in the sequence of 2 black, 4 white and 3 red is
  A)
                  \[\frac{1}{1260}\] done clear
  B)
                  \[\frac{1}{7560}\] done clear
  C)
                  \[\frac{1}{126}\]   done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer98)
  A dice is rolled three times, the probability of getting a larger number than the previous number each time is
  A)
                  \[\frac{15}{216}\] done clear
  B)
                  \[\frac{5}{54}\] done clear
  C)
                  \[\frac{13}{216}\] done clear
  D)
                  \[\frac{1}{18}\] done clear
  View Solution play_arrow

• question_answer99)
  Cards are drawn one by one without replacement from a pack of 52 cards. The probability that 10 cards will precede the first ace is
  A)
                  \[\frac{241}{1456}\]            done clear
  B)
                  \[\frac{164}{4165}\] done clear
  C)
                  \[\frac{451}{884}\]              done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer100)
  The probability that a teacher will give an unannounced test during any class meeting is 1/5. If a student is absent twice, then the probability that the student will miss at least one test is
  A)
                  \[\frac{4}{5}\]        done clear
  B)
                  \[\frac{2}{5}\] done clear
  C)
                  \[\frac{7}{5}\]        done clear
  D)
                  \[\frac{9}{25}\] done clear
  View Solution play_arrow

• question_answer101)
  The chances of throwing a total of 3 or 5 or 11 with two dice is                        [Kurukshetra CEE 1996]
  A)
                  \[\frac{5}{36}\]     done clear
  B)
                  \[\frac{1}{9}\] done clear
  C)
                  \[\frac{2}{9}\]        done clear
  D)
                  \[\frac{19}{36}\] done clear
  View Solution play_arrow

• question_answer102)
  A six faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. The probability that the sum of two numbers thrown is even, is              [Kurukshetra CEE 1996]
  A)
                  \[\frac{1}{12}\]     done clear
  B)
                  \[\frac{1}{6}\] done clear
  C)
                  \[\frac{1}{3}\]        done clear
  D)
                  \[\frac{2}{3}\] done clear
  View Solution play_arrow

• question_answer103)
  The chance of India winning toss is 3/4. If it wins the toss, then its chance of victory is 4/5 otherwise it is only 1/2. Then chance of India's victory is [Kurukshetra CEE 1998]
  A)
                  \[\frac{1}{5}\]        done clear
  B)
                  \[\frac{3}{5}\] done clear
  C)
                  \[\frac{3}{40}\]     done clear
  D)
                  \[\frac{29}{40}\] done clear
  View Solution play_arrow

• question_answer104)
  From a pack of 52 cards one card is drawn at random, the probability that it is either a king or a queen is
  A)
                  \[\frac{1}{13}\]     done clear
  B)
                  \[\frac{2}{13}\] done clear
  C)
                  \[\frac{3}{13}\]     done clear
  D)
                  \[\frac{4}{13}\] done clear
  View Solution play_arrow

• question_answer105)
  From a pack of 52 cards, two cards are drawn one by one without replacement. The probability that first drawn card is a king and second is a queen, is [MP PET 1997]
  A)
                  \[\frac{2}{13}\]     done clear
  B)
                  \[\frac{8}{663}\] done clear
  C)
                  \[\frac{4}{663}\]   done clear
  D)
                  \[\frac{103}{663}\] done clear
  View Solution play_arrow

• question_answer106)
  The probabilities of a student getting I, II and III division in an examination are respectively \[\frac{1}{10},\,\frac{3}{5}\] and \[\frac{1}{4}.\] The probability that the student fails in the examination is [MP PET 1997]
  A)
                  \[\frac{197}{200}\]              done clear
  B)
                  \[\frac{27}{100}\] done clear
  C)
                  \[\frac{83}{100}\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer107)
  An unbiased die is tossed until a number greater than 4 appears. The probability that an even number of tosses is needed is                                            [IIT 1994]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{2}{5}\] done clear
  C)
                  \[\frac{1}{5}\]        done clear
  D)
                  \[\frac{2}{3}\] done clear
  View Solution play_arrow

• question_answer108)
  Two dice are thrown together. The probability that at least one will show its digit 6 is                                [RPET 1996]
  A)
                  \[\frac{11}{36}\]   done clear
  B)
                  \[\frac{36}{11}\] done clear
  C)
                  \[\frac{5}{11}\]     done clear
  D)
                  \[\frac{1}{6}\] done clear
  View Solution play_arrow

• question_answer109)
  A bag contains 30 balls numbered from 1 to 30, one ball is drawn randomly. The probability that number on the ball is multiple of 5 or 7 is                                             [RPET 1997]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{1}{3}\] done clear
  C)
                  \[\frac{2}{3}\]        done clear
  D)
                  \[\frac{1}{4}\] done clear
  View Solution play_arrow

• question_answer110)
  A person can kill a bird with probability 3/4. He tries 5 times. What is the probability that he may not kill the bird  [RPET 1997]
  A)
                  \[\frac{243}{1024}\]            done clear
  B)
                  \[\frac{781}{1024}\] done clear
  C)
                  \[\frac{1}{1024}\] done clear
  D)
                  \[\frac{1023}{1024}\] done clear
  View Solution play_arrow

• question_answer111)
  A fair coin is tossed repeatedly. If tail appears on first four tosses then the probability of head appearing on fifth toss equals                                               [IIT 1998]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{1}{32}\] done clear
  C)
                  \[\frac{31}{32}\]   done clear
  D)
                  \[\frac{1}{5}\] done clear
  View Solution play_arrow

• question_answer112)
  A coin is tossed 3 times by 2 persons. What is the probability that both get equal number of heads         [DCE 1999]
  A)
                  \[\frac{3}{8}\]        done clear
  B)
                  \[\frac{1}{9}\] done clear
  C)
                  \[\frac{5}{16}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer113)
  The sum of two positive numbers is 100. The probability that their product is greater than 1000 is         [RPET 1999]
  A)
                  \[\frac{7}{9}\]        done clear
  B)
                  \[\frac{7}{10}\] done clear
  C)
                  \[\frac{2}{5}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer114)
  The corners of regular tetrahedrons are numbered 1, 2, 3, 4. Three tetrahedrons are tossed.  The probability that the sum of upward corners will be 5 is                                              [AMU 1999]
  A)
                  \[\frac{5}{24}\]     done clear
  B)
                  \[\frac{5}{64}\] done clear
  C)
                  \[\frac{3}{32}\]     done clear
  D)
                  \[\frac{3}{16}\] done clear
  View Solution play_arrow

• question_answer115)
  An integer is chosen at random and squared. The probability that the last digit of the square is 1 or 5 is                 [AMU 1999]
  A)
                  \[\frac{2}{10}\]     done clear
  B)
                  \[\frac{3}{10}\] done clear
  C)
                  \[\frac{4}{10}\]     done clear
  D)
                  \[\frac{9}{25}\] done clear
  View Solution play_arrow

• question_answer116)
  Two integers are chosen at random and multiplied. The probability that the product is an even integer is [AMU 1999]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{2}{3}\] done clear
  C)
                  \[\frac{3}{4}\]        done clear
  D)
                  \[\frac{4}{5}\] done clear
  View Solution play_arrow

• question_answer117)
  A binary number is made up of 16 bits. The probability of an incorrect bit appearing is p and the errors in different bits are independent of one another. The probability of forming an incorrect number is                                     [AMU 1999]
  A)
                  \[\frac{p}{16}\]     done clear
  B)
                  \[{{p}^{16}}\] done clear
  C)
                  \[{}^{16}{{C}_{1}}{{p}^{16}}\] done clear
  D)
                  \[1-{{(1-p)}^{16}}\] done clear
  View Solution play_arrow

• question_answer118)
  A coin is tossed 4 times. The probability that at least one head turns up is                                   [MP PET 2000]
  A)
                  \[\frac{1}{16}\]     done clear
  B)
                  \[\frac{2}{16}\] done clear
  C)
                  \[\frac{14}{16}\]   done clear
  D)
                  \[\frac{15}{16}\] done clear
  View Solution play_arrow

• question_answer119)
  The probability that in a year of the 22nd century chosen at random there will be 53 Sundays is               [Orissa JEE 2003]
  A)
                  \[\frac{3}{28}\]     done clear
  B)
                  \[\frac{2}{28}\] done clear
  C)
                  \[\frac{7}{28}\]     done clear
  D)
                  \[\frac{5}{28}\] done clear
  View Solution play_arrow

• question_answer120)
  Suppose that a die (with faces marked 1 to 6) is loaded in such a manner that for K = 1, 2, 3?., 6, the probability of the face marked K turning up when die is tossed is proportional to K. The probability of the event that the outcome of a toss of the die will be an even number is equal to                                                              [AMU 2000]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{4}{7}\] done clear
  C)
                  \[\frac{2}{5}\]        done clear
  D)
                  \[\frac{1}{21}\] done clear
  View Solution play_arrow

• question_answer121)
  What is the probability that when one  die is thrown, the number appearing on top is even                      [AMU 2000]
  A)
                  \[\frac{1}{6}\]        done clear
  B)
                  \[\frac{1}{3}\] done clear
  C)
                  \[\frac{1}{2}\]        done clear
  D)
    None of these done clear
  View Solution play_arrow

• question_answer122)
  From a pack of 52 cards two cards are drawn in succession one by one without replacement. The probability that both are aces is                                    [RPET 2001]
  A)
                  \[\frac{2}{13}\]     done clear
  B)
                  \[\frac{1}{51}\] done clear
  C)
                  \[\frac{1}{221}\]   done clear
  D)
                  \[\frac{2}{21}\] done clear
  View Solution play_arrow

• question_answer123)
  Three coins are tossed together, then the probability of getting at least one head is     [RPET 2001; MP PET 1989]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{3}{4}\] done clear
  C)
                  \[\frac{1}{8}\]        done clear
  D)
                  \[\frac{7}{8}\] done clear
  View Solution play_arrow

• question_answer124)
  A pair of a dice thrown, if 5 appears on at least one of the dice, then the probability that the sum is 10 or greater is [MP PET 2001]
  A)
                  \[\frac{11}{36}\]   done clear
  B)
                  \[\frac{2}{9}\] done clear
  C)
                  \[\frac{3}{11}\]     done clear
  D)
                  \[\frac{1}{12}\] done clear
  View Solution play_arrow

• question_answer125)
  In a college, 25% of the boys and 10% of the girls offer Mathematics. The girls constitute 60% of the total number of students. If a student is selected at random and is found to be studying Mathematics, the probability that the student is a girl, is                                              [MP PET 2001]
  A)
                  \[\frac{1}{6}\]        done clear
  B)
                  \[\frac{3}{8}\] done clear
  C)
                  \[\frac{5}{8}\]        done clear
  D)
                  \[\frac{5}{6}\] done clear
  View Solution play_arrow

• question_answer126)
  If two dice are thrown simultaneously then probability that  1 comes on first dice is                                    [RPET 2002]
  A)
                  \[\frac{1}{36}\]     done clear
  B)
                  \[\frac{5}{36}\] done clear
  C)
                  \[\frac{1}{6}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer127)
  If any four numbers are selected and they are multiplied, then the probability that the last digit will be 1, 3, 5 or 7 is [RPET 2002]
  A)
                  \[\frac{4}{625}\]   done clear
  B)
                  \[\frac{18}{625}\] done clear
  C)
                  \[\frac{16}{625}\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer128)
  If a coin be tossed n times then probability that the head comes odd times is [RPET 2002]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{1}{{{2}^{n}}}\] done clear
  C)
                  \[\frac{1}{{{2}^{n-1}}}\]  done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer129)
  The probability that a leap year will have 53 Fridays or 53 Saturdays is                                       [MP PET 2002]
  A)
                  \[\frac{2}{7}\]        done clear
  B)
                  \[\frac{3}{7}\] done clear
  C)
                  \[\frac{4}{7}\]        done clear
  D)
                  \[\frac{1}{7}\] done clear
  View Solution play_arrow

• question_answer130)
  Find the probability that the two digit number formed by digits 1, 2, 3, 4, 5 is divisible by 4 (while repetition of digit is allowed) [UPSEAT 2002]
  A)
                  \[\frac{1}{30}\]     done clear
  B)
                  \[\frac{1}{20}\] done clear
  C)
                  \[\frac{1}{40}\]     done clear
  D)
    None of these done clear
  View Solution play_arrow

• question_answer131)
  Two cards are drawn without replacement from a well-shuffled pack. Find the probability that one of them is an ace of heart                                             [UPSEAT 2002]
  A)
                  \[\frac{1}{25}\]     done clear
  B)
                  \[\frac{1}{26}\] done clear
  C)
                  \[\frac{1}{52}\]     done clear
  D)
    None of these done clear
  View Solution play_arrow

• question_answer132)
  A problem in Mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2, 1/3 and 1/4.  Probability that the problem is solved is [RPET 2001; AIEEE 2002]
  A)
                  \[\frac{3}{4}\]        done clear
  B)
                  \[\frac{1}{2}\] done clear
  C)
                  \[\frac{2}{3}\]        done clear
  D)
                  \[\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer133)
  The chance of getting a doublet with 2 dice is [Kurukshetra CEE 2002]
  A)
                  \[\frac{2}{3}\]        done clear
  B)
                  \[\frac{1}{6}\] done clear
  C)
                  \[\frac{5}{6}\]        done clear
  D)
                  \[\frac{5}{36}\] done clear
  View Solution play_arrow

• question_answer134)
  The chance of throwing a total of 7 or 12 with 2 dice,  is [Kurukshetra CEE 2002]
  A)
                  \[\frac{2}{9}\]        done clear
  B)
                  \[\frac{5}{9}\] done clear
  C)
                  \[\frac{5}{36}\]     done clear
  D)
                  \[\frac{7}{36}\] done clear
  View Solution play_arrow

• question_answer135)
  There are 10 pairs of shoes in a cupboard from which 4 shoes are picked at random. The probability that there is at least one pair, is
  A)
                  \[\frac{99}{323}\] done clear
  B)
                  \[\frac{224}{323}\] done clear
  C)
                  \[\frac{100}{323}\]              done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer136)
  A bag contains 3 red and 7 black balls, two balls are taken out at random, without replacement. If the first ball taken out is red, then what is the probability that the second taken out ball is also red                                                 [Pb. CET 2000]
  A)
                  \[\frac{1}{10}\]     done clear
  B)
                  \[\frac{1}{15}\] done clear
  C)
                  \[\frac{3}{10}\]     done clear
  D)
                  \[\frac{2}{21}\] done clear
  View Solution play_arrow

• question_answer137)
  The probability that a leap year selected randomly will have 53 Sundays is [MP PET 1991, 93, 95; Pb. CET 2002]
  A)
                  \[\frac{1}{7}\]        done clear
  B)
                  \[\frac{2}{7}\] done clear
  C)
                  \[\frac{4}{53}\]     done clear
  D)
                  \[\frac{4}{49}\] done clear
  View Solution play_arrow

• question_answer138)
  A bag contains 3 white and 2 black balls and another bag contains 2 white and 4 black balls. A ball is picked up randomly. The probability of its being black is  [MP PET 1989]
  A)
                  \[\frac{2}{5}\]        done clear
  B)
                  \[\frac{8}{15}\] done clear
  C)
                  \[\frac{6}{11}\]     done clear
  D)
                  \[\frac{2}{3}\] done clear
  View Solution play_arrow

• question_answer139)
  A bag x contains 3 white balls and 2 black balls and another bag y contains 2 white balls and 4 black balls. A bag and a ball out of it are picked at random. The probability that the ball is white, is                                              [IIT 1971]
  A)
                  3/5          done clear
  B)
                  7/15 done clear
  C)
                  1/2          done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer140)
  A box containing 4 white pens and 2 black pens. Another box containing 3 white pens and 5 black pens. If one pen is selected from  each box, then the probability that both the pens are white is equal to                                  [Pb.CET 2002]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{1}{3}\] done clear
  C)
                  \[\frac{1}{4}\]        done clear
  D)
                  \[\frac{1}{5}\] done clear
  View Solution play_arrow

• question_answer141)
  A bag contains 3 red and 5 black balls and a second bag contains 6 red and 4 black balls. A ball is drawn from each bag. The probability that one is red and other is black, is [AISSE 1986]
  A)
                  \[\frac{3}{20}\]     done clear
  B)
                  \[\frac{21}{40}\] done clear
  C)
                  \[\frac{3}{8}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer142)
  The probability that a marksman will hit a target is given as 1/5. Then his probability of at least one hit in 10 shots, is
  A)
                  \[1-{{\left( \frac{4}{5} \right)}^{10}}\]            done clear
  B)
                  \[\frac{1}{{{5}^{10}}}\] done clear
  C)
                  \[1-\frac{1}{{{5}^{10}}}\]               done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer143)
  Four coins are tossed. The probability that at least one head turns up, is                                      [DSSE 1981]
  A)
                  1/16        done clear
  B)
                  1/4 done clear
  C)
                  15/16      done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer144)
  Five horses are in a race.  Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is                                             [AIEEE 2003]
  A)
                  \[\frac{4}{5}\]        done clear
  B)
                  \[\frac{3}{5}\] done clear
  C)
                  \[\frac{1}{5}\]        done clear
  D)
                  \[\frac{2}{5}\] done clear
  View Solution play_arrow

• question_answer145)
  ?X? speaks truth in 60% and ?Y? in 50% of the cases. The probability that they contradict each other narrating the same incident is                                     [UPSEAT 2004]
  A)
                  \[\frac{1}{4}\]        done clear
  B)
                  \[\frac{1}{3}\] done clear
  C)
                  \[\frac{1}{2}\]        done clear
  D)
                  \[\frac{2}{3}\] done clear
  View Solution play_arrow

• question_answer146)
  The probability that A speaks truth is \[\frac{4}{5}\], while this probability for B is \[\frac{3}{4}\]. The probability that they contradict each other when asked to speak on a fact [AIEEE 2004; MP PET 1997, 2002; IIT 1975; MNR 1987]
  A)
                  \[\frac{4}{5}\]        done clear
  B)
                  \[\frac{1}{5}\] done clear
  C)
                  \[\frac{7}{20}\]     done clear
  D)
                  \[\frac{3}{20}\] done clear
  View Solution play_arrow

• question_answer147)
  Probability of throwing 16 in one throw with three dice is [UPSEAT 2004]
  A)
                  \[\frac{1}{36}\]     done clear
  B)
                  \[\frac{1}{18}\] done clear
  C)
                  \[\frac{1}{72}\]     done clear
  D)
                  \[\frac{1}{9}\] done clear
  View Solution play_arrow

• question_answer148)
  The probability of choosing at random a number that is divisible by 6 or 8 from among 1 to 90 is equal to                 [Pb. CET 2002]
  A)
                  \[\frac{1}{6}\]        done clear
  B)
                  \[\frac{1}{30}\] done clear
  C)
                  \[\frac{11}{80}\]   done clear
  D)
                  \[\frac{23}{90}\] done clear
  View Solution play_arrow

• question_answer149)
  The probabilities of a problem being solved by two students are \[\frac{1}{2},\frac{1}{3}\]. Then the probability of the problem being solved is                                                                 [Pb. CET 2001]
  A)
                  \[\frac{2}{3}\]        done clear
  B)
                  \[\frac{4}{3}\] done clear
  C)
                  \[\frac{1}{3}\]        done clear
  D)
                  1 done clear
  View Solution play_arrow

• question_answer150)
  Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three  apply for the same house is                                                [AIEEE 2005]
  A)
                  \[\frac{8}{9}\]        done clear
  B)
                  \[\frac{7}{9}\] done clear
  C)
                  \[\frac{2}{9}\]        done clear
  D)
                  \[\frac{1}{9}\] done clear
  View Solution play_arrow

• question_answer151)
  In a throw of a dice the probability of getting one in even number of throw is                                              [IIT Screening 2005]
  A)
                  \[\frac{5}{36}\]     done clear
  B)
                  \[\frac{5}{11}\] done clear
  C)
                  \[\frac{6}{11}\]     done clear
  D)
                  \[\frac{1}{6}\] done clear
  View Solution play_arrow

• question_answer152)
  A and B are two independent events such that \[P(A)=1/2\]and\[P(B)=1/3\]. Then P (neither A nor B) is equal to                [J & K 2005]
  A)
                  2/3          done clear
  B)
                  1/6 done clear
  C)
                  5/6          done clear
  D)
                  1/3 done clear
  View Solution play_arrow

• question_answer153)
  Consider the circuit,                 If the probability that each switch is closed is p, then find the probability of current flowing through AB [DCE 2005]
  A)
                  \[{{p}^{2}}+p\] done clear
  B)
                  \[{{p}^{3}}+p-1\] done clear
  C)
                  \[{{p}^{3}}+p\] done clear
  D)
                  \[{{p}^{2}}+p+1\] done clear
  View Solution play_arrow