Question

Compare the hypergeometric and binomial distributions. Suppose there is a sock drawer with N socks, each placed loosely in the drawer (not rolled into pairs). The total number of black socks is m. You take out a random sample of n < m socks. Assume all the socks are the same shape, size, etc. and that each sock is equally likely to be chosen.

Suppose the sampling is done without replacement. Calculate the probability of getting at least 2 black socks (your goal in order to wear matching black socks that day...) under the following conditions: N = 10, n = 4, m = 5.

Answer 1