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 Mutually Exclusive Definition

Mutually exclusive events cannot occur at the same time (i.e., \( P(A \cap B) = 0 \)). For two events \( A \) (rolling a 6) and \( B \) (rolling an even number), check if they can overlap.

Step2: Analyze Event Overlap

Even numbers on a die are 2, 4, 6. So rolling a 6 (event \( A \)) is also an even number (event \( B \)). Thus, \( A \cap B=\{6\} \), so \( P(A \cap B)>0 \).

Answer:

The events (rolling a 6 or rolling an even number) are not mutually exclusive because a roll of 6 is both a 6 and an even number, meaning the events can occur simultaneously.