Question

Given that P(A)=0,7; P(B)=0,4 and P(A and B)=0,28, are events A and B mutually exclusive? Give a reason for your answer. are the events A and B independent? Give a reason for your answer.

Answer 1

For two events to be mutually exclusive, with event A and B, the probability of their union is the sum of the probabilities of the events.

P(A∪B)=P(A)+P(B)

0.28 is not = 0.7 + 0.4 = 1.10 , therefore A and B are not mutually exclusive, they can happen at same time.

Two events, A and B are independent if and only if:

P(A and B)=P(A)×P(B)

0.28 = 0.7 x 0.4 = 0.28 , therefore independent.