Let A and B be two events such that the probability that exactly one of them occurs is ${2 \over 5}$ and the probability that A or B occurs is ${1 \over 2}$ , then the probability of both of them occur together is :

Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(x = 4), then the sum of the mean and the variance of X is…

Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If…

Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random…

If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then ${{P(X = 2)} \over {P(X = 3)}}$ is…

Let a die be rolled $n$ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers…