Question

If two events, E and F, are mutually exclusive with probabilities P(E) = 0.3 and P(F) = 0.2, what is the probability of event E occurring given that event F has occurred, represented as P(E | F)?

Answer 1

Since events E and F are mutually exclusive, the probability of E occurring given that F has occurred, P(E | F), is 0 because mutually exclusive events cannot happen simultaneously.

Step-by-step explanation:

If two events, E and F, are mutually exclusive events, they cannot occur at the same time. By definition, this means that if event F occurs, event E cannot happen, and vice versa. Therefore, the probability of E occurring given that F has already occurred, denoted as P(E | F), is 0 because we know for a fact that once F has happened, E cannot possibly happen.

To emphasize, mutually exclusive events have no overlap in their outcomes; they are completely separate. So the rule for conditional probability does not apply here because the condition (F occurring) makes the probability of E impossible.