Probability distributions binomial or hypergeometric

[xdrgnh]

Homework Statement

A committee of 16 persons is selected randomly from a group of 400 people, of whom are 240 are women and 160 are men. Approximate the probability that the committe contains at least 3 women.



I just want to know if it's hyper geometric or binomial. I suspect it's hyper geometric because if you pick 1 person from total 400 people you alter the probability of picking the next person thus it's not independent.

 

[Ray Vickson]

Homework Statement

A committee of 16 persons is selected randomly from a group of 400 people, of whom are 240 are women and 160 are men. Approximate the probability that the committe contains at least 3 women.



I just want to know if it's hyper geometric or binomial. I suspect it's hyper geometric because if you pick 1 person from total 400 people you alter the probability of picking the next person thus it's not independent.

You are correct. However, in cases where populations of both types are large compared with the total sample size, the hypergeometric and the binomial give nearly the same results, at least if we do not ask for results far out in the 'tails'. In this case, we want 1-P{<= 2 women}, and the '2' is far below the mean. That means that the binomial approximation may not be so good in this case, even though the committee size 16 is small compared to both 160 and 240.