Chapter 13, Problem 1E

Pet ownership Suppose that 25% of people have a dog, 29% of people have a cat, and 12% of people own both. What is the probability that someone owns a dog or a cat?

To determine

Find the probability that one owns a dog or a cat.

Answer to Problem 1E

The probability that one owns a dog or a cat is 0.42.

Explanation of Solution

Given info:

There are 25% of people who have a dog, 29% of people who have a cat, and 12% of people have both dog and cat.

Calculation:

General addition rule of probability:

$P\left(A\text{ or }B\right)=P\left(A\right)+P\left(B\right)-P\left(A\text{ and }B\right)$

Here, 25% of people own a dog. Hence, the probability of selecting a person who owns a dog is 0.25. Similarly, the probability of selecting a person who owns a cat is 0.29 and the probability of selecting a person who owns both dog and cat is 0.12. The required probability is the probability that one owns a dog or a cat is obtained as follows:

$\begin{array}{c}P\left(\text{Dog or cat}\right)=P\left(\text{Dog}\right)+P\left(\text{Cat}\right)-P\left(\text{Dog and Cat}\right)\\ =0.25+0.29-0.12\\ =0.42\end{array}$

Thus, the probability that one owns a dog or a cat is 0.42.