Chapter 13.6, Problem 12PPS

To determine

To determine whether the events are mutually exclusive or not mutually exclusive. Also find probability.

Answer to Problem 12PPS

Not mutually exclusive.

Probability is $\frac{4}{13}$ or 30.8%

Explanation of Solution

Given information :

Drawing an ace or a heart from a standard deck of 52 cards.

Two events can be mutually exclusive if there is no common outcome of the both events. Whereas if there is any common outcome then the events becomes not mutually exclusive events.

Here the outcome may be an ace of heart, which is common to both events. Hence the events are not mutually exclusive.

Total outcomes are 52.

Probability of drawing an ace is $\frac{4}{52}$

Probability of getting a heart is $\frac{13}{52}$

Now,

P(ace and heart) $=\frac{1}{52}$ (ace of heart is the common outcome)

P(ace or heat) $=\frac{4}{52}+\frac{13}{52}-\text{P(ace and heart)}$

P(ace or heat) $=\frac{4}{52}+\frac{13}{52}-\frac{1}{52}=\frac{4}{13}$ or 30.8%