Chapter 11.8, Problem 24E

To determine

TO-DETERMINE the probability that a randomly chosen member of the population owned a cat or a dog.

Answer to Problem 24E

The probability of a randomly chosen member of the population owning a cat or a dog is $\text{P}\left(\text{A or B}\right)=27\%$ .

Explanation of Solution

Given information:

Consider, $19\%$ of the population owned dogs, so the probability of owning a dog is $\text{P}\left(\text{A}\right)=19\%$ .

  $14\%$ of the population owned cats, so the probability of owning a cat is $\text{P}\left(\text{B}\right)=14\%$ .

  $6\%$ of the population owned both, $\text{P}\left(\text{A and B}\right)=6\%$ .

Calculation:

Some people owned both a cat and a dog, so the events are overlapping.

  $\begin{array}{l}\text{P}\left(\text{A or B}\right)=\text{P}\left(\text{A}\right)+\text{P}\left(\text{B}\right)-\text{P}\left(\text{A and B}\right)\left[\text{Probability of overlapping events}\right]\\ \text{P}\left(\text{A or B}\right)=19\%+14\%-6\%\left[\text{Substitute the probabilities}\right]\\ \text{P}\left(\text{A or B}\right)=27\%\left[\text{Simplify}\right]\end{array}$

Hence, The probability of a randomly chosen member of the population owning a cat or a dog is $\text{P}\left(\text{A or B}\right)=27\%$ .