Question

During a given month, P(A)=0.75,P(B)=0.6, and P(A and B)=0.5. Are these two events independent? Are they mutually exclusive? A. yes;yes B. yes;no. no;yes C. no;no. D. it cannot be determined

Answer 1

Two events are mutually exclusive when the probability that both events happen equals the product of the probability that both events happen individually.
i.e. P(A and B) = P(A) x P(B)
Here, P(A and B) = 0.5 but P(A) x P(B) = 0.75 x 0.6 = 0.45
Therefore, the two events are not independent.

Two events are said to be mutually exclusive when P(A and B) = 0. Here P(A and B) ≠ 0.
Therefore, the two events are not mutually exclusive.

Therefore, option C is the correct answer.