JEE Main & Advanced Mathematics Probability Question Bank

done Use of permutations and combinations in probability Total Questions - 81

• question_answer1)
  Two cards are drawn at random from a pack of 52 cards. The probability that both are the cards of spade is
  A)
             \[\frac{1}{26}\]                        done clear
  B)
             \[\frac{1}{4}\] done clear
  C)
             \[\frac{1}{17}\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer2)
  Six cards are drawn simultaneously from a pack of playing cards. What is the probability that 3 will be red and 3 black
  A)
             \[^{26}{{C}_{6}}\]               done clear
  B)
             \[\frac{^{26}{{C}_{3}}}{^{52}{{C}_{6}}}\] done clear
  C)
             \[\frac{^{26}{{C}_{3}}{{\times }^{26}}{{C}_{3}}}{^{52}{{C}_{6}}}\]               done clear
  D)
             \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer3)
  A man draws a card from a pack of 52 playing cards, replaces it and shuffles the pack. He continues this processes until he gets a card of spade. The probability that he will fail the first two  times  is                                           [MNR 1980]
  A)
             \[\frac{9}{16}\]                        done clear
  B)
             \[\frac{1}{16}\] done clear
  C)
             \[\frac{9}{64}\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer4)
  If out of 20 consecutive whole numbers two are chosen at random, then the probability that their sum is odd, is
  A)
             \[\frac{5}{19}\]                        done clear
  B)
             \[\frac{10}{19}\] done clear
  C)
             \[\frac{9}{19}\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer5)
  A bag contains 3 red, 7 white and 4 black balls. If three balls are drawn from the bag, then the probability that all of them are of the same colour is
  A)
             \[\frac{6}{71}\]                        done clear
  B)
             \[\frac{7}{81}\] done clear
  C)
             \[\frac{10}{91}\]                      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer6)
  If four persons are chosen at random from a group of  3 men, 2 women and 4 children. Then the probability that exactly two of them are children, is [Kurukshetra CEE 1996; DCE 1999]
  A)
             \[\frac{10}{21}\]                      done clear
  B)
             \[\frac{8}{63}\] done clear
  C)
             \[\frac{5}{21}\]                        done clear
  D)
             \[\frac{9}{21}\] done clear
  View Solution play_arrow

• question_answer7)
  A box contains 25 tickets numbered 1, 2, ....... 25. If two tickets are drawn at random then the probability that the product of their numbers  is even, is
  A)
             \[\frac{11}{50}\]                      done clear
  B)
             \[\frac{13}{50}\] done clear
  C)
             \[\frac{37}{50}\]                      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer8)
  From a class of 12 girls and 18 boys, two students are chosen randomly. What is the probability that both of them are girls
  A)
             \[\frac{22}{145}\]                    done clear
  B)
             \[\frac{13}{15}\] done clear
  C)
             \[\frac{1}{18}\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer9)
  A word consists of 11 letters in which there are 7 consonants and 4 vowels. If 2 letters are chosen at random, then the probability that all of them are consonants, is
  A)
             \[\frac{5}{11}\]                        done clear
  B)
             \[\frac{21}{55}\] done clear
  C)
             \[\frac{4}{11}\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer10)
  Twenty tickets are marked the numbers 1, 2, ..... 20. If three tickets be drawn at random, then what is the probability that those marked  7 and 11 are among them
  A)
             \[\frac{3}{190}\]                      done clear
  B)
             \[\frac{1}{19}\] done clear
  C)
             \[\frac{1}{190}\]                      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer11)
  If Mohan has 3 tickets of a lottery containing 3 prizes and 9 blanks, then his chance of winning prize are
  A)
             \[\frac{34}{55}\]                      done clear
  B)
             \[\frac{21}{55}\] done clear
  C)
             \[\frac{17}{55}\]                      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer12)
  A bag contains 3 white and 7 red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red
  A)
             0     done clear
  B)
             \[\frac{3}{10}\] done clear
  C)
             \[\frac{7}{10}\]                        done clear
  D)
             \[\frac{10}{10}\] done clear
  View Solution play_arrow

• question_answer13)
  A bag contains  4 white, 5 red and 6 black balls. If two balls are drawn at random, then the probability that one of them is white is
  A)
             \[\frac{44}{105}\]                    done clear
  B)
             \[\frac{11}{105}\] done clear
  C)
             \[\frac{11}{21}\]                      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer14)
  A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, then the probability that 2 are white and 1 is red, is
  A)
             \[\frac{5}{204}\]                      done clear
  B)
             \[\frac{7}{102}\] done clear
  C)
             \[\frac{3}{68}\]                        done clear
  D)
             \[\frac{1}{13}\] done clear
  View Solution play_arrow

• question_answer15)
  A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all, is      [CEE 1993]
  A)
             \[\frac{1}{2}\]                           done clear
  B)
             \[\frac{5}{9}\] done clear
  C)
             \[\frac{4}{9}\]                           done clear
  D)
             \[\frac{2}{9}\] done clear
  View Solution play_arrow

• question_answer16)
  The letter of the word `ASSASSIN' are written down at random in a row. The probability that no two S occur together is    [BIT Ranchi 1990; IIT 1983]
  A)
             \[\frac{1}{35}\]                        done clear
  B)
             \[\frac{1}{14}\] done clear
  C)
             \[\frac{1}{15}\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer17)
  The probability of getting 4 heads in 8 throws of a coin, is
  A)
             \[\frac{1}{2}\]                           done clear
  B)
             \[\frac{1}{64}\] done clear
  C)
             \[\frac{^{8}{{C}_{4}}}{8}\]       done clear
  D)
             \[\frac{^{8}{{C}_{4}}}{{{2}^{8}}}\] done clear
  View Solution play_arrow

• question_answer18)
  In a lottery 50 tickets are sold in which 14 are of prize. A man bought 2 tickets, then the probability that the man win the prize, is
  A)
             \[\frac{17}{35}\]                      done clear
  B)
             \[\frac{18}{35}\] done clear
  C)
             \[\frac{72}{175}\]                    done clear
  D)
             \[\frac{13}{175}\] done clear
  View Solution play_arrow

• question_answer19)
  A bag contains 8 black and 7 white balls. Two balls are drawn at random. Then for which the probability is more
  A)
             Both balls are white done clear
  B)
             One ball is white and one is black done clear
  C)
             Both balls are black done clear
  D)
             All of the above are equals done clear
  View Solution play_arrow

• question_answer20)
  A committee has to be made of 5 members from 6 men and 4 women. The probability that at least one woman is present in committee, is
  A)
             \[\frac{1}{42}\]                        done clear
  B)
             \[\frac{41}{42}\] done clear
  C)
             \[\frac{2}{63}\]                        done clear
  D)
             \[\frac{1}{7}\] done clear
  View Solution play_arrow

• question_answer21)
  A three digit number is formed by using numbers 1, 2, 3 and 4. The probability that the number is divisible by 3, is
  A)
             \[\frac{2}{3}\]                           done clear
  B)
             \[\frac{2}{7}\] done clear
  C)
             \[\frac{1}{2}\]                           done clear
  D)
             \[\frac{3}{4}\] done clear
  View Solution play_arrow

• question_answer22)
  From a pack of playing cards three cards are drawn simultaneously. The probability that these are one king, one queen and one jack is
  A)
             \[\frac{64}{5525}\]                 done clear
  B)
             \[\frac{16}{5525}\] done clear
  C)
             \[\frac{128}{5525}\]               done clear
  D)
             \[\frac{64}{625}\] done clear
  View Solution play_arrow

• question_answer23)
  Word ?UNIVERSITY? is arranged randomly. Then the probability that both ?I? does not come together, is [UPSEAT 2001]
  A)
             \[\frac{3}{5}\]                           done clear
  B)
             \[\frac{2}{5}\] done clear
  C)
             \[\frac{4}{5}\]                           done clear
  D)
             \[\frac{1}{5}\] done clear
  View Solution play_arrow

• question_answer24)
  There are n different objects 1, 2, 3,......n distributed at random in n places marked 1, 2, 3, ......n. The probability that at least three of the objects occupy places corresponding to their number is
  A)
             \[\frac{1}{6}\]                           done clear
  B)
             \[\frac{5}{6}\] done clear
  C)
             \[\frac{1}{3}\]                           done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer25)
  An ordinary cube has four blank faces, one face marked 2 another marked 3. Then the probability of obtaining a total of exactly 12 in 5 throws, is
  A)
             \[\frac{5}{1296}\]                    done clear
  B)
             \[\frac{5}{1944}\] done clear
  C)
             \[\frac{5}{2592}\]                    done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer26)
  Two persons each make a single throw with a die. The probability they get equal value is\[{{p}_{1}}\]. Four persons each make a single throw and probability of three being equal is\[{{p}_{2}}\], then
  A)
             \[{{p}_{1}}={{p}_{2}}\]      done clear
  B)
             \[{{p}_{1}}<{{p}_{2}}\] done clear
  C)
             \[{{p}_{1}}>{{p}_{2}}\]      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer27)
  n cadets have to stand in a row. If all possible permutations are equally likely, then the probability that two particular cadets stand side by side, is
  A)
             \[\frac{2}{n}\]                           done clear
  B)
             \[\frac{1}{n}\] done clear
  C)
             \[\frac{2}{(n-1)\,!}\]                 done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer28)
  A bag contains tickets numbered from 1 to 20. Two tickets are drawn. The probability that both the numbers are prime, is                                                                               [AISSE 1981]
  A)
             \[\frac{14}{95}\]                      done clear
  B)
             \[\frac{7}{95}\] done clear
  C)
             \[\frac{1}{95}\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer29)
  A bag contains 6 red, 5 white and 4 black balls. Two balls are drawn. The probability that none of them is red, is [AI CBSE 1983]
  A)
             \[\frac{12}{35}\]                      done clear
  B)
             \[\frac{6}{35}\] done clear
  C)
             \[\frac{4}{35}\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer30)
  A bag contains 3 white and 5 black balls. If one ball is drawn, then the probability that it is black, is        [RPET 1995]
  A)
    \[\frac{3}{8}\]                                    done clear
  B)
    \[\frac{5}{8}\] done clear
  C)
             \[\frac{6}{8}\]                           done clear
  D)
    \[\frac{10}{20}\] done clear
  View Solution play_arrow

• question_answer31)
  Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, is equal to [IIT 1995; MP PET 2002, 04]
  A)
             \[\frac{1}{2}\]                           done clear
  B)
             \[\frac{1}{5}\] done clear
  C)
             \[\frac{1}{10}\]                        done clear
  D)
             \[\frac{1}{20}\] done clear
  View Solution play_arrow

• question_answer32)
  Three mangoes and three apples are in a box. If two fruits are chosen at random, the probability that one is a mango and the other is an apple is                                                         [EAMCET 1990]
  A)
             \[\frac{2}{3}\]                           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_answer33)
  There are 5 volumes of Mathematics among 25 books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is
  A)
             \[\frac{1}{5\,!}\]                        done clear
  B)
             \[\frac{50\,!}{55\,!}\] done clear
  C)
             \[\frac{1}{{{50}^{5}}}\]      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer34)
  A cricket team has 15 members, of whom only 5 can bowl. If the names of the 15 members are  put into a hat and 11 drawn at random, then the chance of obtaining an eleven containing at least 3 bowlers is
  A)
    \[\frac{7}{13}\]                                  done clear
  B)
    \[\frac{11}{15}\] done clear
  C)
             \[\frac{12}{13}\]                      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer35)
  A bag has 13 red, 14 green and 15 black balls. The probability of getting exactly 2 blacks on pulling out 4 balls is \[{{P}_{1}}.\]Now the number of each colour ball is doubled and 8 balls are pulled out. The probability of getting exactly 4 blacks is  \[{{P}_{2}}.\] Then
  A)
             \[{{P}_{1}}={{P}_{2}}\]      done clear
  B)
             \[{{P}_{1}}>{{P}_{2}}\] done clear
  C)
             \[{{P}_{1}}<{{P}_{2}}\]      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer36)
  If m rupee coins and n ten paise coins are placed in a line, then the probability that the extreme coins are ten paise coins is
  A)
             \[^{m+n}{{C}_{m}}/{{n}^{m}}\]                                      done clear
  B)
             \[\frac{n\,(n-1)}{(m+n)\,(m+n-1)}\] done clear
  C)
             \[^{m+n}{{P}_{m}}/{{m}^{n}}\]                                       done clear
  D)
             \[^{m+n}{{P}_{n}}/{{n}^{m}}\] done clear
  View Solution play_arrow

• question_answer37)
  A mapping is selected at random from the set of all the mappings of the set \[A=\left\{ 1,\,\,2,\,...,\,n \right\}\]into itself. The probability that the mapping selected is an injection is
  A)
    \[\frac{1}{{{n}^{n}}}\]                  done clear
  B)
    \[\frac{1}{n\,!}\] done clear
  C)
    \[\frac{(n-1)\,!}{{{n}^{n-1}}}\]     done clear
  D)
             \[\frac{n\,!}{{{n}^{n-1}}}\] done clear
  View Solution play_arrow

• question_answer38)
  A lot consists of 12 good pencils, 6 with minor defects and 2 with major defects. A pencil is choosen at random. The probability that this pencil is not defective is [EAMCET 1991]
  A)
             \[\frac{3}{5}\]                           done clear
  B)
             \[\frac{3}{10}\] done clear
  C)
             \[\frac{4}{5}\]                           done clear
  D)
             \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer39)
  A box contains 10 mangoes out of which 4 are rotten. 2 mangoes are taken out together. If one of them is found to be good, the probability that the other is also good is [EAMCET 1992]
  A)
             \[\frac{1}{3}\]                           done clear
  B)
             \[\frac{8}{15}\] done clear
  C)
             \[\frac{5}{18}\]                        done clear
  D)
             \[\frac{2}{3}\] done clear
  View Solution play_arrow

• question_answer40)
  Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman is                                                            [ISM Dhanbad 1994]
  A)
             \[\frac{25}{39}\]                      done clear
  B)
             \[\frac{14}{39}\] done clear
  C)
             \[\frac{5}{13}\]                        done clear
  D)
             \[\frac{10}{13}\] done clear
  View Solution play_arrow

• question_answer41)
  Two numbers a and b are chosen at random from the set of first 30 natural numbers. The probability that \[{{a}^{2}}-{{b}^{2}}\]is divisible by 3 is
  A)
             \[\frac{9}{87}\]                        done clear
  B)
             \[\frac{12}{87}\] done clear
  C)
             \[\frac{15}{87}\]                      done clear
  D)
             \[\frac{47}{87}\] done clear
  View Solution play_arrow

• question_answer42)
  Two friends A and B have equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of A and B. The probability that all the tickets go to daughters of A is 1/20. The number of daughters each of them have is
  A)
             4     done clear
  B)
             5 done clear
  C)
             6     done clear
  D)
             3 done clear
  View Solution play_arrow

• question_answer43)
  Dialing a telephone number an old man forgets the last two digits remembering only that these are different dialled at random. The probability that the number is dialled correctly, is
  A)
             \[\frac{1}{45}\]                        done clear
  B)
             \[\frac{1}{90}\] done clear
  C)
             \[\frac{1}{100}\]                      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer44)
  In a box there are 2 red, 3 black and 4 white balls. Out of these three balls are drawn together. The probability of these being of same colour is                                                                   [MP PET 1996]
  A)
             \[\frac{1}{84}\]                        done clear
  B)
             \[\frac{1}{21}\] done clear
  C)
             \[\frac{5}{84}\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer45)
  Six boys and six girls sit in a row randomly. The probability that the six girls sit together
  A)
             \[\frac{1}{77}\]                        done clear
  B)
             \[\frac{1}{132}\] done clear
  C)
             \[\frac{1}{231}\]                      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer46)
  From a group of 7 men and 4 ladies a committee of 6 persons is formed, then the probability that the committee contains 2 ladies is
  A)
             \[\frac{5}{13}\]                        done clear
  B)
             \[\frac{5}{11}\] done clear
  C)
             \[\frac{4}{11}\]                        done clear
  D)
             \[\frac{3}{11}\] done clear
  View Solution play_arrow

• question_answer47)
  A bag contains 4 white and 3 red balls. Two draws of one ball each are made without replacement. Then the probability that both the balls are red is
  A)
             \[\frac{1}{7}\]                           done clear
  B)
             \[\frac{2}{7}\] done clear
  C)
             \[\frac{3}{7}\]                           done clear
  D)
             \[\frac{4}{7}\] done clear
  View Solution play_arrow

• question_answer48)
  A bag contains 5 white, 7 black and 4 red balls. Three balls are drawn from the bag at random. The probability that all the three balls are white, is     [MP PET 1997]
  A)
             \[\frac{3}{16}\]                        done clear
  B)
             \[\frac{3}{5}\] done clear
  C)
             \[\frac{1}{60}\]                        done clear
  D)
             \[\frac{1}{56}\] done clear
  View Solution play_arrow

• question_answer49)
  Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is                    [MP PET 1997; Pb. CET 2000]
  A)
             \[\frac{14}{29}\]                      done clear
  B)
             \[\frac{20}{39}\] done clear
  C)
             \[\frac{1}{2}\]                           done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer50)
  The probability that the three cards drawn from a pack of 52 cards are all red is                                          [MP PET 1999]
  A)
             \[\frac{1}{17}\]                        done clear
  B)
             \[\frac{3}{19}\] done clear
  C)
             \[\frac{2}{19}\]                        done clear
  D)
             \[\frac{2}{17}\] done clear
  View Solution play_arrow

• question_answer51)
  A committee consists of 9 experts taken from three institutions A, B and C, of which 2 are from A, 3 from B and 4 from C. If three experts resign, then the probability that they belong to different institutions is [Roorkee Qualifying 1998]
  A)
             \[\frac{1}{729}\]                      done clear
  B)
             \[\frac{1}{24}\] done clear
  C)
             \[\frac{1}{21}\]                        done clear
  D)
             \[\frac{2}{7}\] done clear
  View Solution play_arrow

• question_answer52)
  Two numbers are selected at random from 1, 2, 3 ......100 and are multiplied, then the probability correct to two places of decimals that the product thus obtained is divisible by 3, is                                                          [Kurukshetra CEE 1998]
  A)
             0.55 done clear
  B)
             0.44 done clear
  C)
             0.22                                           done clear
  D)
             0.33 done clear
  View Solution play_arrow

• question_answer53)
  Five digit numbers are formed using the digits 1, 2, 3, 4, 5, 6 and 8.  What is the probability that they have even digits at both the ends                                                                      [RPET 1999]
  A)
             \[\frac{2}{7}\]                           done clear
  B)
             \[\frac{3}{7}\] done clear
  C)
             \[\frac{4}{7}\]                           done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer54)
  A bag contains 3 red, 4 white and 5 black balls. Three balls are drawn at random. The probability of being their different colours is                                                                [RPET 1999]
  A)
             \[\frac{3}{11}\]                        done clear
  B)
             \[\frac{2}{11}\] done clear
  C)
             \[\frac{8}{11}\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer55)
  If four vertices of a regular octagon are chosen at random, then the probability that the quadrilateral  formed by them is a rectangle is                                                                         [AMU 1999]
  A)
             \[\frac{1}{8}\]                           done clear
  B)
             \[\frac{2}{21}\] done clear
  C)
             \[\frac{1}{32}\]                        done clear
  D)
             \[\frac{1}{35}\] done clear
  View Solution play_arrow

• question_answer56)
  A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour is                                   [UPSEAT 1999; MP PET 2000]
  A)
             \[\frac{5}{108}\]                      done clear
  B)
             \[\frac{18}{108}\] done clear
  C)
             \[\frac{30}{108}\]                    done clear
  D)
             \[\frac{48}{108}\] done clear
  View Solution play_arrow

• question_answer57)
  If a committee of 3 is to be chosen from a group of 38 people of which you are a member. What is the probability that you will be on the committee                                             [AMU 2000]
  A)
  \[\left( \begin{align}   & 38 \\  & \,3 \\ \end{align} \right)\]                             done clear
  B)
  \[\left( \begin{align}   & 37 \\  & \,2 \\ \end{align} \right)\] done clear
  C)
  \[\left( _{2}^{37} \right)/\left( _{3}^{38} \right)\] done clear
  D)
  \[\frac{666}{8436}\] done clear
  View Solution play_arrow

• question_answer58)
  Four boys and three girls stand in a queue for an interview, probability that they will in alternate position is                    [UPSEAT 2001]
  A)
             \[\frac{1}{34}\]                        done clear
  B)
             \[\frac{1}{35}\] done clear
  C)
             \[\frac{1}{17}\]                        done clear
  D)
             \[\frac{1}{68}\] done clear
  View Solution play_arrow

• question_answer59)
  In a lottery there were 90 tickets numbered 1 to 90. Five tickets were drawn at random. The probability that two of the tickets drawn numbers 15 and 89 is                                         [AMU 2001]
  A)
             \[\frac{2}{801}\]                      done clear
  B)
             \[\frac{2}{623}\] done clear
  C)
             \[\frac{1}{267}\]                      done clear
  D)
             \[\frac{1}{623}\]   done clear
  View Solution play_arrow

• question_answer60)
  Among 15 players, 8 are batsmen and 7 are bowlers. Find the probability that a team is chosen of 6 batsmen and 5 bowlers                                                                          [UPSEAT 2002]
  A)
             \[\frac{{}^{8}{{C}_{6}}\times {}^{7}{{C}_{5}}}{{}^{15}{{C}_{11}}}\]             done clear
  B)
             \[\frac{^{8}{{C}_{6}}{{+}^{7}}{{C}_{5}}}{^{15}{{C}_{11}}}\] done clear
  C)
             \[\frac{15}{28}\]                      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer61)
  A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomwise, the probability that it is a black or red ball is                                                                      [EAMCET 2002]
  A)
             \[\frac{1}{3}\]                           done clear
  B)
             \[\frac{1}{4}\] done clear
  C)
             \[\frac{5}{12}\]                        done clear
  D)
             \[\frac{2}{3}\] done clear
  View Solution play_arrow

• question_answer62)
  Out of 30 consecutive numbers, 2 are chosen at random.  The probability that their sum is odd, is [Kurukshetra CEE 2002]
  A)
             \[\frac{14}{29}\]                      done clear
  B)
             \[\frac{16}{29}\] done clear
  C)
             \[\frac{15}{29}\]                      done clear
  D)
             \[\frac{10}{29}\] done clear
  View Solution play_arrow

• question_answer63)
  Three integers are chosen at random from the first 20 integers. The probability that their product is even, is           [Kurukshetra CEE 2002]
  A)
             \[\frac{2}{19}\]                        done clear
  B)
             \[\frac{3}{29}\] done clear
  C)
             \[\frac{17}{19}\]                      done clear
  D)
             \[\frac{4}{19}\] done clear
  View Solution play_arrow

• question_answer64)
  Two numbers are selected randomly from the set \[S=\{1,\,2,\,3,\,4,\,5,\,6\}\] without replacement one by one. The probability that minimum of the two numbers is less than 4 is [IIT Screening 2003]
  A)
             \[\frac{1}{15}\]                        done clear
  B)
             \[\frac{14}{15}\] done clear
  C)
             \[\frac{1}{5}\]                           done clear
  D)
             \[\frac{4}{5}\] done clear
  View Solution play_arrow

• question_answer65)
  A bag contains 6 white, 7 red and 5 black balls. If 3 balls are drawn from the bag at random, then the probability that all of  them are white is
  A)
             \[\frac{20}{204}\]                    done clear
  B)
             \[\frac{5}{204}\] done clear
  C)
             \[\frac{1}{3}\]                           done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer66)
  A bag contains 4 white, 5 red and 6 green balls. Three balls are picked up randomly. The probability that a white, a red and a green ball is drawn is
  A)
             \[\frac{15}{91}\]                      done clear
  B)
             \[\frac{30}{91}\] done clear
  C)
             \[\frac{20}{91}\]                      done clear
  D)
             \[\frac{24}{91}\] done clear
  View Solution play_arrow

• question_answer67)
  A box contains 10 red balls and 15 green balls. If two balls are drawn in succession then the probability that one is red and other is green, is
  A)
             \[\frac{1}{3}\]                           done clear
  B)
             \[\frac{1}{2}\] done clear
  C)
             \[\frac{1}{4}\]                           done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer68)
  Three cards are drawn at random from a pack of 52 cards. What is the chance of drawing three aces
  A)
             \[\frac{3}{5525}\]                    done clear
  B)
             \[\frac{2}{5525}\] done clear
  C)
             \[\frac{1}{5525}\]                    done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer69)
  A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random. The probability that at least one of these is an ace, is                                               [MNR 1991]
  A)
             \[\frac{9}{20}\]                        done clear
  B)
             \[\frac{3}{16}\] done clear
  C)
             \[\frac{1}{6}\]                           done clear
  D)
             \[\frac{1}{9}\] done clear
  View Solution play_arrow

• question_answer70)
  A fair coin is tossed 100 times. The probability of getting tails an odd number of times is
  A)
           \[\frac{1}{2}\]                        done clear
  B)
             \[\frac{1}{8}\] done clear
  C)
             \[\frac{3}{8}\]                           done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer71)
  A bag contains 3 red, 4 white and 5 blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour is                                                [EAMCET 1987]
  A)
             \[\frac{47}{66}\]                      done clear
  B)
             \[\frac{10}{33}\] done clear
  C)
             \[\frac{5}{22}\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer72)
  Ten students are seated at random in a row. The probability that two particular students are not seated side by side is
  A)
             \[\frac{4}{5}\]                           done clear
  B)
             \[\frac{3}{5}\] done clear
  C)
             \[\frac{2}{5}\]                           done clear
  D)
             \[\frac{1}{5}\] done clear
  View Solution play_arrow

• question_answer73)
  A drawer contains 5 brown socks and 4 blue socks well mixed. A man reaches the drawer and pulls out 2 socks at random. What is the probability that they match
  A)
             \[\frac{4}{9}\]                           done clear
  B)
             \[\frac{5}{8}\] done clear
  C)
             \[\frac{5}{9}\]                           done clear
  D)
             \[\frac{7}{12}\] done clear
  View Solution play_arrow

• question_answer74)
  5 persons A, B, C, D and E are in queue of a shop. The probability that A and E always together, is
  A)
             \[\frac{1}{4}\]                           done clear
  B)
             \[\frac{2}{3}\] done clear
  C)
             \[\frac{2}{5}\]                           done clear
  D)
             \[\frac{3}{5}\] done clear
  View Solution play_arrow

• question_answer75)
  A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is                                                               [UPSEAT 2004]
  A)
             \[\frac{14}{15}\]                      done clear
  B)
             \[\frac{11}{15}\] done clear
  C)
             \[\frac{7}{15}\]                        done clear
  D)
             \[\frac{4}{15}\] done clear
  View Solution play_arrow

• question_answer76)
  From eighty cards numbered 1 to 80, two cards are selected randomly. The probability that both the cards have the numbers divisible by 4 is given by [Pb. CET 2000]
  A)
             \[\frac{21}{316}\]                    done clear
  B)
           \[\frac{19}{316}\] done clear
  C)
             \[\frac{1}{4}\]                           done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer77)
  A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. One fruit is picked out from each basket. Find the probability that the fruits are both apples or both oranges                               [AMU 2002]
  A)
             \[\frac{24}{144}\]                    done clear
  B)
             \[\frac{56}{144}\] done clear
  C)
             \[\frac{68}{144}\]                    done clear
  D)
             \[\frac{76}{144}\] done clear
  View Solution play_arrow

• question_answer78)
  Let A and B be two finite sets having m and n elements respectively such that \[m\le n.\,\] A mapping is selected at random from the set of all mappings from A to B. The probability that the mapping selected is an injection is
  A)
             \[\frac{n\,!}{(n-m)\,!\,{{m}^{n}}}\]                                         done clear
  B)
             \[\frac{n\,!}{(n-m)\,!\,{{n}^{m}}}\] done clear
  C)
             \[\frac{m\,!}{(n-m)\,!\,{{n}^{m}}}\]                                        done clear
  D)
             \[\frac{m\,!}{(n-m)\,!\,{{m}^{n}}}\] done clear
  View Solution play_arrow

• question_answer79)
  Suppose \[n\ge 3\] persons are sitting in a row. Two of them are selected at random. The probability that they are not together is                                                                    [Pb. CET 2004]
  A)
           \[1-\frac{2}{n}\]                     done clear
  B)
             \[\frac{2}{n-1}\] done clear
  C)
             \[1-\frac{1}{n}\]                       done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer80)
  Fifteen persons among whom are A and B, sit down at random at a round table. The probability that there are 4 persons between A and B, is
  A)
             \[\frac{1}{3}\]                           done clear
  B)
             \[\frac{2}{3}\] done clear
  C)
             \[\frac{2}{7}\]                           done clear
  D)
             \[\frac{1}{7}\] done clear
  View Solution play_arrow

• question_answer81)
  5 boys and 5 girls are sitting in a row randomly. The probability that boys and girls sit alternatively is  [Kerala (Engg.) 2005]
  A)
             5/126                                         done clear
  B)
             1/126 done clear
  C)
             4/126                                         done clear
  D)
             6/125 done clear
  E)
             1/63 done clear
  View Solution play_arrow