Question

example 1
determine whether the events are mutually exclusive or not mutually exclusive. explain
your reasoning.

1. a die is rolled while a game is being played. the result of the next roll is a 6 or an

even number.

Explanation:

Step1: Recall mutual exclusive definition

Mutually exclusive events cannot occur at the same time, i.e., \( P(A \cap B) = 0 \).

Step2: Analyze the two events

Event \( A \): Rolling a 6. Event \( B \): Rolling an even number (2, 4, 6). The intersection \( A \cap B \) is rolling a 6 (since 6 is in both events), so \( P(A \cap B)
eq 0 \).

Answer:

The events are not mutually exclusive. Because rolling a 6 (event 1) and rolling an even number (event 2) can happen simultaneously (as 6 is an even number), so they are not mutually exclusive.