# [SOLVED] Probability

• Dec 4th 2008, 04:51 PM
fabxx
[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?

• Dec 4th 2008, 05:15 PM
nzmathman
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