Question

At a comic book shop, about 3/5 of the customers are male and about 2/3 are under the age of 40. It is also known that about 5/8 of the customers are female or over the age of 40. What is the probability that a customer selected at random is female and over the age of 40?

Answer 1

Given that, At a comic book shop, about 3/5 of the customers are male and about 2/3 are under the age of 40. It is also known that about 5/8 of the customers are female or over the age of 40.

That is, P(male) = 3/5

P( under the age of 40) = 2/3

P(female OR over the age of 40) = 5/8

P(female) = 1 - P(male) = 1 - 3/5 = 2/5

P(over the age of 40)=1 - P(under the age of 40)= 1 - 2/3 = 1/3

We want to find, P(female AND ovet the age of 40)

We know,

P(Female OR over the age of 40)

= P(Female) + P(over the age of 40) - P(Female AND over the age of 40)

=> 5/8 = (2/5) + (1/3) - P(Female AND over the age of 40)

=> P(Female AND over the age of 40) = (2/5) + (1/3) - (5/8)

=> P(Female AND over thebage of 40) = 13/120 = 0.1083

Therefore, the probability that a customer selected at random is female and over the age of 40 is 13/120 = 0.1083