Probability that a man speaks truth is $\frac{3}{4}$. He throws a die and reports that it is a six. The probability that it is actually a six is

If A and B are two distinct events such that P(A|B) = P(B|A), then which of the following is /are possible?

(A) A= B

(B) P (A) = P(B)

(C) A ⊂ B but A ≠ B

(D) A∩ B = ɸ

Choose the correct answer from the options given below:

Three students A, B and C can respectively solve 50%, 25% and 20% of the problems in a book. A particular problem is selected at random from the book. The probability that at least one of them will solve the problem is

Let X denotes the number of heads in a simultaneous toss of three coins, then $P(0 < X < 3)$ is

The probability distribution of a random variable X is given by

If $a > 0$, then $P(0 < x \leq 2)$ is equal to

Let box I contains 3 black and 4 white balls, box II contains 2 black and 2 white balls, box III contains 4 black and 3 white balls. A box is selected at random and then a ball is randomly drawn from the selected box. If the color of the ball is black then the probability that the ball is drawn from box III, is:

If the probability of two successes is 9 times the probability of 3 successes in 3 trials of a binomial distribution, then the probability of success in each trial is: