Probability questions
692 published questions with worked solutions.
- Let S = w_1, w_2,……. be the sample space associated to a random experiment. Let P(w_n) = P(w_ n-1 ) 2 , n 2. Let A = 2k+3l : k, N...
- A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the...
- Let A be the event that the absolute difference between two randomly chosen real numbers in the sample space [0, 60] is less than...
- A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag...
- One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional...
- Let H_1, H_2, , H_n be mutually exclusive and exhaustive events with P(H_i) > 0, i = 1, 2, …, n. Let E be any other event with 0...
- Let E^c denote the complement of an event E. Let E, F, G be pairwise independent events with P(G) > 0 and P(E F G) = 0. Then...
- Three students S_1, S_2, and S_3 are given a problem to solve. Consider the following events: U: At least one of S_1, S_2, and...
- 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...
- A and B are events such that P(A B) = 3/4, P(A B) = 1/4, P( A) = 2/3 then P( A B) is
- A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is
- The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then P (X = 1) is
- Events A, B, C are mutually exclusive events such that P(A) = 3x+1 3 , P(B) = x-1 4 and P(C) = 1-2x 4 . The set of possible...
- 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...
- The probability that A speaks truth is 4 5 , while this probability for B is 3 4 . The probability that they contradict each...
- A random variable X has the probability distribution: X: 1, 2, 3, 4, 5, 6, 7, 8; p(X): 0.15, 0.23, 0.12, 0.10, 0.20, 0.08, 0.07,...
- The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
- Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting...
- A random variable X has Poisson distribution with mean 2. Then P(X > 1.5) equals
- A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is
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