Chapter 12.5, Problem 16PPS

To determine

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

Answer to Problem 16PPS

The events are mutually exclusive and the probability that Dario will select either a baseball or a football card is $\frac{247}{295}\text{ or 83}\text{.7\%}$ .

Explanation of Solution

Given information:

The given statement is:

“Dario owns $145$ baseball cards, $102$ football cards and $48$ basketball cards. What is the probability that he randomly selects a baseball or a football card?”

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 Dario cannot select both a baseball and a football card.

The probability can be calculated by;

  $\begin{array}{l}\text{P}\left(\text{baseball}\right)=\frac{145}{295}\\ \text{P}\left(\text{football}\right)=\frac{102}{295}\\ \text{P}\left(\text{baseball or football}\right)=\frac{145}{295}+\frac{102}{295}\\ \text{P}\left(\text{baseball or football}\right)=\frac{247}{295}\text{ or 83}\text{.7\%}\end{array}$

Hence, the events are mutually exclusive and the probability that Dario will select either a baseball or a football card is $\frac{247}{295}\text{ or 83}\text{.7\%}$ .