Chapter 12.5, Problem 6CYU

To determine

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

Answer to Problem 6CYU

The events are mutually exclusive and the probability $\text{P}\left(\text{diamond or heart}\right)=\frac{1}{2}\text{ or 50\%}$ .

Explanation of Solution

Given information:

The given statement is:

  $\text{P}\left(\text{diamond or heart}\right)$

Formula used:

The following formula is used:

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

Calculation :

The events are mutually exclusive because a card cannot be both a diamond and a heart.

The probability can be calculated by;

  $\begin{array}{l}\text{P}\left(\text{diamond}\right)=\frac{13}{52}\\ \text{P}\left(\text{heart}\right)=\frac{13}{52}\\ \text{P}\left(\text{diamond or heart}\right)=\frac{13}{52}+\frac{13}{52}\\ \text{P}\left(\text{diamond or heart}\right)=\frac{26}{52}\\ \text{P}\left(\text{diamond or heart}\right)=\frac{1}{2}\text{ or 50\%}\end{array}$

Hence, the events are mutually exclusive and the probability $\text{P}\left(\text{diamond or heart}\right)=\frac{1}{2}\text{ or 50\%}$ .