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question_answer1) A box contains tickets numbered from 1 to 20. Three tickets are drawn from the box with replacement. The probability that the largest number on the tickets is 7 is
question_answer2) A man has 3 pairs of black socks and 2 pairs of brown socks kept together in a box. If he dressed hurriedly in the dark, the probability that after he has put on a black sock, he will then put on another black sock is
question_answer3) A natural number is chosen at random from the first 100 natural numbers. The probability that \[x+\frac{100}{x}>50\] is
question_answer4) A sample space consists of 3 sample points with associated probabilities given as \[2p,\,\,{{p}^{2}},\,\,4p-1\]. Then the value of p is
question_answer5) There are only two women among 20 persons taking part in a pleasure trip. The 20 persons are divided into two groups, each group consisting of 10 persons. Then the probability that the two women will be in the same group is
question_answer6) The probabilities of winning a race by three persons A, B, and C are 1/2, 1/4, and 1/4, respectively. They run two races. The probability of A winning the second race when B, wins the first race is
question_answer7) A and B toss a fair coin each simultaneously 50 times. The probability that both of them will not get tail at the same toss is
question_answer8) Three ships A, B, and C sail from England to India. If the ratio of their arriving safely are 2:5, 3:7, and 6:11, respectively, then the probability of all the ships for arriving safely is
question_answer9) There are 20 cards. Ten of these cards have the letter "I" printed on them and the other 10 have the letter "T" printed on them. If three cards are picked up at random and kept in the same order, the probability of making word IIT is
question_answer10) The probability that a bulb produced by a factory will fuse after 150 days if used is 0.50. What is the probability that out of 5 such bulbs none will fuse after 150 days of use?
question_answer11) If a is an integer lying in [\[-\]5, 30], then the probability that the graph \[y={{x}^{2}}+2\,(a+4)x-5a+64\] is strictly above the x-axis is
question_answer12) 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
question_answer13) In a certain town, 40% of the people have brown hair, 25% have brown eyes, and 15% have both brown hair and brown eyes. If a person selected at random from the town has brown hair, the probability that he also has brown eyes is
question_answer14) In a n-sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is
question_answer15) 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
question_answer16) A doctor is called to see a sick child. The doctor knows (prior to the visit) that 90% of the sick children in that neighborhood are sick with the flu, denoted by F, while 10% are sick with the measles, denoted by M. A well-known symptom of measles is a rash, denoted by R. The probability of having a rash for a child sick with the measles is 0.95. However, occasionally children with the flu also develop a rash, with conditional probability 0.08. Upon examination the child, the doctor finds a rash. Then what is the probability that the child has the measles?
question_answer17) Let A and B are events of an experiment and \[P(A)=1/4,\,\,P(A\cup B)=1/2\] then value of \[P(B/{{A}^{c}})\] is
question_answer18) A fair die is tossed repeatedly. A wins if it is 1 or 2 on two consecutive tosses and B wins if it is 3, 4, 5 or 6 on two consecutive tosses. The probability that A wins if the die is tossed indefinitely is
question_answer19) Forty teams play a tournament. Each team plays every other team just once. Each game results in a win for one team. If each team has a 50% chance of winning each game, the probability that at the end of the tournament, every team has won a different number of games is
question_answer20) There are 10 prizes, five A's, three B's, and two C's, placed in identical sealed envelopes for the top 10 contestants in a mathematics contest. The prizes are awarded by allowing winners to select an envelope at random from those remaining. When the 8th contestant goes to select the prize, the probability that the remaining three prizes are one A, one B and one C is
question_answer21) An artillery target may be either at point I with probability 8/9 or at point II with probability 1/9. We have 55 shells, each of which can be fired either rat point I or II. Each shell may hit the target, independent of the other shells, with probability 1/2. Maximum number of shells must be fired at point I to have maximum probability is _______.
question_answer22) There are 3 bags. Bag 1 contains 2 red and\[{{a}^{2}}-4a+8\] black balls, bag 2 contains 1 red and \[{{a}^{2}}-4a+9\] black balls, and bag 3 containa 3 red and \[{{a}^{2}}-4a+7\] black balls. A ball is drawn at random from at random chosen bag. Then the maximum value of probability that it is a red ball is ______.
question_answer23) A problem in mathematics is given to three students A, B, and C and their respective probability of solving the problem is 1/2, 1/3, and 1/4. The probability that the problem is solved is ______.
question_answer24) A die is tossed five times. Getting an odd number is considered a success. Then the variance of distribution of success is ____.
question_answer25) The probability that A speaks truth is 4/5, while this probability for B is 3/4. The probability that they contradict each other when asked to speak on a fact is ____.
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