Chapter 13, Problem 1E

To determine

Compute the probability that someone owns a dog or a cat.

Answer to Problem 1E

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

Explanation of Solution

Calculation:

Among people, 25% have a dog, 29% have a cat, and 12% have both dog and cat.

Additive rule of probability:

For any two events A and B, the addition rule is as follows:

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

Define event A as people who have a dog and event B as people who have a cat.

In this situation, $P\left(A\right)=0.25,P\left(B\right)=0.29,\text{and }P\left(A\text{ and }B\right)=0.12$. Substitute these values in the above equation.

The required probability is obtained as shown below:

$\begin{array}{c}P\left(\text{dog}\text{or cat}\right)=P\left(A\text{ or }B\right)\\ =0.25+0.29-0.12\\ =0.42\end{array}$

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