Suppose two events A and B are mutually exclusive, with P(A) ≠ 0 and P(B) ≠ 0. By working through the following steps, you’ll see why two mutually exclusive events are not independent.
(a) For mutually exclusive events, can event A occur if event B has occurred? What is the value of P(A | B)?
(b) Using the information from part (a), can you conclude that events A and B are not independent if they are mutually exclusive? Explain.