Given two independent events A and B that are not mutually e

Given two independent events, A and B, that are not mutually exclusive and P(A)=0.4 and P(B)=0.5, then P(A or B) equals ??

Solution

not mutually exclusive => P(A and B) is not zero.

P(A or B) = P(A) + P(B) - P(A and B) = 0.4 + 0.5 - P(A and B)

P(A or B) = 0.9 - P(A and B)

Also, the events are independent, P(A and B) = 0.4 * 0.5 = 0.2

P(A or B) = 0.9 - 0.2 = 0.7

P(A or B) = 0.7