Chapter 13.4, Problem 27E

To determine

To find whether the pair of events is mutually exclusive or mutually inclusive and find the probability.

Answer to Problem 27E

Mutually inclusive, $\frac{8}{13}$

Explanation of Solution

Given:

The probability of selecting a red or a face card.

Calculation:

The standard cards contains $26$ red cards, $4$ aces ( $2$ red and $2$ black). In total there are $52$ cards

Let $A$ be the event ofselecting a red card.

Let $B$ be the event ofselecting a face card.

Sample space $52$

The events are mutually inclusive as there can be a red face card.

Therefore probability of event $A$ is $P(A)=\frac{26}{52}$

And probability of event $B$ is $P(B)=\frac{12}{52}$

Hence,

  $\begin{array}{l}P(\text{A or B})=P(A)+P(B)-P(A\text{ and }B\text{)}\\ P(\text{A Or B})=\frac{26}{52}+\frac{12}{52}-\frac{6}{52}=\frac{8}{13}\end{array}$