Question

In a clothing store, 65% of the customers buy a shirt, 30% of the customers

buy a pair of pants, and 20% of the customers buy both a shirt and a pair of
pants.
If a customer is chosen at random, what is the probability that he or she buys
a shirt or a pair of pants?

Answer 1

75%

Explanation:

List out known probabilities

`\Pr(shirt) = 0.65 = (65)/(100) = (13)/(20)\\ \Pr(pants) = 0.40 = (30)/(100) = (6)/(20)\\\Pr(shirt \cap pants) = 0.20 = (20)/(100)=(1)/(5)`

recall equation

`\Pr(A \cup B)=\Pr(A)+\Pr(B)-\Pr(A \cap B)`

Plug in values

`\Pr(shirt \cup pants)=(13)/(20)+(6)/(20)-(1)/(5)\\\\therefore \Pr(shirt \cup pants) = (15)/(20) =(3)/(4) = 75\%`