13.2: What is the probability that a randomly selected person in the country enjoys cooking or shopping or​ both?

Question

Fifty-four percent of people in a certain country like to cook and 52​% of people in the country like to​ shop, while 22​% enjoy both activities. What is the probability that a randomly selected person in the country enjoys cooking or shopping or​ both?

The probability that a randomly selected person in the country enjoys cooking or shopping or both is _________.

​(Type an integer or a decimal. Do not​ round.)

Answer 1

draw a Venn diagram

make 2 overlapping circles

the overlap is .22= those who shop and cook

.54-.22 = .32 = those who shop but don't cook

.52-.22 = .30 = those who cook but don't shop

.30+.32+.22 = .84 = those who shop or cook or do both = 84%

Answer 2

Event A = enjoy cooking

Event B = enjoy shopping

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

P(A or B) = 0.54 + 0.52 - 0.22 = 0.84