Question

The probability distribution of a random variable X is given below :

A and B are independent events such that P(A ∩ B̄) = 1/4 and P(Ā ∩ B) = 1/6. Find P(A) and P(B).

From a lot of 30 bulbs which include 6 defective bulbs, a sample of 2 bulbs is drawn at random one by one with replacement. Find the probability distribution of the number of defective bulbs and hence find the mean number of defective bulbs.

Probabilities of A and B solving a specific problem are 2/3 and 3/5, respectively. If both of them try independently to solve the problem, then find the probability that the problem is solved.