If A and B are mutually exclusive events such that P (A) = and P (B) = , then find P(A ∪ B).

A bag contains 12 balls out of which x balls are white. (i) If one ball is drawn at random, what is the probability that it will be a white ball. (ii) If 6 more white balls are put in the bag and if the probability of drawing a white ball will be twice that of in (i), then find x.

Piggy bank contains 100 fifty-paise coins, 50 one-rupee coins, 20 two-rupees coins and 10 five- rupees coins. One coin is drawn at random. Find the probability that the drawn coin

(i) will be a fifty-paise coin (ii) will not be a five-rupees coin.

If A and B are two events such that P (A) = , P (B) = and P(A ∪ B) = , then find P(A ∩ B).

If P (A) = , P (B) = , P(A ∪ B) = 1. Find (i) P(A ∩ B) (ii) P(A’ ∪ B’).