Chapter 12.5, Problem 8CYU

To determine

To state whether the events are mutually exclusive or not mutually exclusive and find the probability.

Answer to Problem 8CYU

The events are not mutually exclusive and the probability $\text{P}\left(\text{spade or ace}\right)=\frac{4}{13}\text{ or 30}\text{.8\%}$ .

Explanation of Solution

Given information:

The given statement is:

  $\text{P}\left(\text{spade or ace}\right)$

Formula used:

The following formula is used:

  $\text{Probability}=\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}$

Calculation :

The events are not mutually exclusive because a card can have both a spade and an ace.

The probability can be calculated by;

  $\begin{array}{l}\text{P}\left(\text{spade}\right)=\frac{13}{52}\\ \text{P}\left(\text{ace}\right)=\frac{4}{52}\\ \text{P}\left(\text{spade and ace}\right)=\frac{1}{52}\\ \text{P}\left(\text{spade or ace}\right)=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}\\ \text{P}\left(\text{spade or ace}\right)=\frac{16}{52}\\ \text{P}\left(\text{spade or ace}\right)=\frac{4}{13}\text{ or 30}\text{.8\%}\end{array}$

Hence, the events are not mutually exclusive and the probability $\text{P}\left(\text{spade or ace}\right)=\frac{4}{13}\text{ or 30}\text{.8\%}$ .