A company of four

Probability Level 4

Someone tells you that a company has 4 employees and at least 2 are women.

The probability that the other two are men is $\dfrac{a}{b}$ , where $a$ and $b$ are coprime positive integers.

What is $a+b$ ?

Assumption: This company has non-discriminatory hiring practices, and thus women and men are equally likely to be hired.

The answer is 17.

1 solution

Geoff Pilling
Nov 5, 2016

If you have the employees line up and number them 1 to 4, and look at all the sixteen possible combinations of women and men they could represent, there are 11 combinations of men and women where you have at least two women.

In six of these combinations the other two are men.

So, the probability is $\frac{6}{11}$ .

$6+11 = \boxed{17}$

It might be worth mentioning that this company has non-discriminatory hiring practices, and thus women and men are equally likely to be hired.

Brian Charlesworth - 4 years, 7 months ago

Ah, good point! :)

Geoff Pilling - 4 years, 7 months ago

A company of four

The answer is 17.

1 solution

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