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Chapter 5: Q. 69. (page 330)

Dogs and cats In one large city, 40%of all households, own a dog, 32%

own a cat, and 18% own both. Suppose we randomly select a household and learn that the household owns a cat. Find the probability that the household owns a dog.

Short Answer

Expert verified

The probability that the household owns a dog is 0.5625

Step by step solution

01

Given information

40%of the households own a dog.
32%of the households own a cat.
18% of the households own both pets.

02

Explanation

Let,

D:own a dog

C: own a cat

The following probabilities correspond:

Probability for owing a dog,
P(D)=0.40

Possibility of having a cat,

P(C)=0.32

Possibility of owning two pets

P(DandC)=0.18

Because the household that was chosen at random owns a cat.

Use the conditional probability formula:

P(D鈭�C)=P(Dand)P(C)=0.180.32=916=0.5625

Therefore, the probability that the randomly selected household owns a dog is 0.5625

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