Chapter 5.3, Problem 69E

To determine

Probability for household owns a dog.

Answer to Problem 69E

Probability that the household owns a dog is 0.5625.

Explanation of Solution

Given information:

40% of the households own a dog.

32% of the households own a cat.

18% of the households own both pets.

Let

D: own a dog

C: own a cat

Corresponding probabilities are:

Probability for owing a dog,

  $P\left(\text{D}\right)=0.40$

Probability for owing a cat,

  $P\left(\text{C}\right)=0.32$

Probability for owing both pets,

  $P\left(\text{D}\text{and}\text{C}\right)=0.18$

Since the randomly selected household owns a cat.

Apply the conditional probability:

  $P\left(\text{D}|\text{C}\right)=\frac{P\left(\text{D}\text{and}\text{C}\right)}{P\left(\text{C}\right)}=\frac{0.18}{0.32}=\frac{9}{16}=0.5625$

Thus,

Probability that the randomly selected household owns a dog is 0.5625.