A is an event with probability pA 25 B is an event with pro

A is an event with probability p(A) = 2/5 B is an event with probability p(B) = 4/5. Select the correct statement from the following three. give a proof for your selection. A, 8, are mutually exclusive events. A, B, are not mutually exclusive events. Insufficient information to determine.

Solution

Note that

P(A U B) <= 1

Thus,

P(A) + P(B) - P(A n B) <= 1

2/5 + 4/5 - P(A n B) <= 1

P(A n B) >= 1/5 > 0

If A and B are mutually exclusive, then P(A n B) = 0.

Thus, OPTION B: A, B ARE NOT MUTUALLY EXCLUSIVE EVENTS. [ANSWER, B]