Probability of solving specific problem independently by A and B are `1/2 and 1/3` respectively. If both try to solve the problem independently, find the probability that
(i) the problem is solved (ii) exactly one of them solves the problem.
One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent?
(i) E: ‘the card drawn is a spade’
F: ‘the card drawn is an ace’
(ii) E: ‘the card drawn is black’
F: ‘the card drawn is a king’
(iii) E: ‘the card drawn is a king or queen’
F: ‘the card drawn is a queen or jack’
If A and B are two independent events such that `P(barA∩ B) =2/15 and P(A ∩ barB) = 1/6`, then find P(A) and P(B).
Given that the events A and B are such that P(A) = 12, PA∪B=35 and P (B) = p. Find p if they are (i) mutually exclusive (ii) independent.