Probability Q: 48 of 120 applicants are women

[bccrusader3]

120 people apply for two jobs. forty-eight of the applicants are women. if two applications are selected at random, what is the probability that only one is a woman's application?

 

[tkhunny]

That is an excellent problem of a very basic Binomial Apptoximation.

Hint: n = 2 and p = 48/120

 

[soroban]

Hello, bccrusader3!

120 people apply for two jobs. Forty-eight of the applicants are women.
if two applications are selected at random, what is the probability that
only one is a woman's application?

\(\displaystyle \text{There are: }\;{120\choose2} \:=\:7140\text{ possible selections.}\)

\(\displaystyle \text{To select one woman and one man, there are: }\:48\cdot72 \:=\: 3456\text{ ways.}\)

\(\displaystyle \text{Therefore: }\;P(\text{one woman}) \;=\;\frac{3456}{7140} \;=\;\boxed{\frac{288}{595}}\)