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Chapter 3: Q3.17 (page 98)

In a certain community, 36 percent of the families own a dog and 22 percent of the families that own a dog also own a cat. In addition, 30 percent of the families own a cat. What is (a) the probability that a randomly selected family owns both a dog and a cat? (b) the conditional probability that a randomly selected family owns a dog given that it owns a cat?

Short Answer

Expert verified

P(DogandCat)=0.0792

P(DogICat)=0.264

Step by step solution

01

Given Information of a & b

Given that in a certain community, 36 percent of the families own a dog and 22 percent of the families that own a dog also own a cat

We have to find the probability that a randomly selected family owns both a dog and a cat

Also, find the conditional probability that a randomly selected family owns a dog given that it owns a cat

02

Explanation

03

Explanation-a

a)P(Dog and Cat)=0.36×0.22

=0.0792

04

Explanation-b

b)P(Dog∣cat)=P(Dog and Cat)P(Cat)

P(cat)=0.30given

P(Dog∣cat)=0.36×0.220.30

=0.264

05

Final Answer of a & b

(a) P(Dog and Cat)=0.0792

(b) P(Dog∣cat)=0.264

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