13.1: Suppose that 20​% of people have a dog​, 32​% of people have a cat​, and 8​% of people own both. What is the probability that someone owns a dog or a cat​?

Question

Suppose that 20​% of people have a dog​, 32​% of people have a cat​, and 8​% of people own both. What is the probability that someone owns a dog or a cat​?

The probability of a person having a dog or a cat is _____.

​(Type an integer or a​ decimal.

Answer 1

Event A = have a dog

Event B = have a cat

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.2 + 0.32 - 0.08 = 0.44

Answer 2

You might draw a Venn diagram, with 2 overlapping circles

the overlapping part is .08

those who own only a dog are .2-.08 = .12

those who own only a cat are .32-.08 = .24

add up .12+.24+.08 = .44 = probability of someone owning a cat or a dog