7.8 Exercise 1

Decide whether the following events are mutually exclusive. If they are not mutually exclusive, identify an outcome that would result in both events occurring.

1. You are about to roll a standard 6-sided die. $E$ is the event “the die shows an even number” and $F$ is the event “the die shows an odd number.”
2. You are about to roll a standard 6-sided die. $E$ is the event “the die shows an even number” and $S$ is the event “the die shows a number less than 4.”
3. You are about to flip a coin 4 times. $J$ is the event “at least 2 heads are flipped” and $K$ is the event “fewer than 3 tails are flipped.”