
[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?
Thanks in advance

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 $\displaystyle \cap$ less than 40yo) = 1/4.
So P(married) = P(married $\displaystyle \cap$ at least 40yo) + P(married $\displaystyle \cap$ less than 40yo)
5/8 = P(married $\displaystyle \cap$ at least 40yo) + 1/4
P(married $\displaystyle \cap$ at least 40yo) = 5/8  1/4 = 3/8
P(at least 40yo) = P(married $\displaystyle \cap$ at least 40yo) + P(not married $\displaystyle \cap$ at least 40yo)
3/4 = 3/8 + P(not married $\displaystyle \cap$ at least 40yo)
Therefore, P(not married $\displaystyle \cap$ at least 40yo) = 3/4  3/8 = 3/8