# Math Help - [SOLVED] Probability

1. ## [SOLVED] Probability

Kaplan Page 136 #23

at a certain factory 5/8 of the workers are married and 3/4 are at least 40 years old. if 1/4 of the married workers are younger than 40, what fraction of the workers who are at least 40 are not married?

The answer is 3/8 Why?

2. Try drawing a venn diagram with 2 overlapping circles; one for married and one for at least 40yo.

You know:
P(married) = 5/8.
P(at least 40yo) = 3/4.
P(married $\cap$ less than 40yo) = 1/4.

So P(married) = P(married $\cap$ at least 40yo) + P(married $\cap$ less than 40yo)
5/8 = P(married $\cap$ at least 40yo) + 1/4

P(married $\cap$ at least 40yo) = 5/8 - 1/4 = 3/8
P(at least 40yo) = P(married $\cap$ at least 40yo) + P(not married $\cap$ at least 40yo)
3/4 = 3/8 + P(not married $\cap$ at least 40yo)

Therefore, P(not married $\cap$ at least 40yo) = 3/4 - 3/8 = 3/8