Suppose two events A and B are independent, with P(A) ≠ 0 and P(B) ≠ 0. By working through the following steps, you'll see why two independent events are not mutually exclusive. (a) What formula is used to compute P(A and B)? P(A) + P(B) P(A) / P(B) P(A) − P(B) P(A) · P(B) Is P(A and B) ≠ 0? Explain. Yes. Even if P(A) = 0 or P(B) = 0, P(A and B) will always be non-zero. No. Because both P(A) and P(B) are not equal to 0, P(A and B) = 0. No. P(A and B) = 0. Yes. Because both P(A) and P(B) are not equal to 0, P(A and B) ≠ 0. (b) Using the information from part (a), can you conclude that events A and B are not mutually exclusive? No. Two events being independent always implies they are mutually exclusive. No. Because P(A and B) ≠ 0, A and B are mutually exclusive. Yes. Two events being independent always implies they are mutually exclusive. Yes. Because P(A and B) ≠ 0, A and B are not mutually exclusive.