Suppose a three-person comittee is formed for a culb by drawing names out of a hat. If the expected number of women is 2 and there are 10 men in the culb, how many women are in the club?

Answer: 20 women

Explanation:

Making the total number of women in the club 'x', we can then do the following,

Total Number of Names in Hat, N

N = x + 10 (total number of men)

therefore total number of names in the hat N=x+10

We need to select 3 people so sample size = 3

Using the Hypergeometric Distribution then we can then use the formula,

Expected number of women on the Committee = k * n / N

Where k is the total number

2 = x * 3 / (x + 10)

2 = 3x / (x + 10)

3x = 2x + 20

x = 20

There are 20 women in the club.