4. For this problem, you’ll compare the hypergeometric andbinomial distributions. Suppose there is a sock drawer with Nsocks, each placed loosely in the drawer (not rolled into pairs).The total number of black socks is m. You take out a random sampleof n < m socks. Assume all the socks are the same shape, size,etc. and that each sock is equally likely to be chosen.
(a) Suppose the sampling is done without replacement. Calculatethe probability of getting at least 2 black socks (your goal inorder to wear matching black socks that day...) under the followingconditions:
(i) N = 10, n = 4, m = 5.
(ii) N = 20, n = 4, m = 10.
(iii) N = 40, n = 4, m = 20.
(b) Suppose the sampling is done with replacement (this doesn’tmake much sense if you are planning to wear the socks!). Calculatethe probability of getting at least two black socks when you samplefour socks and the proportion of black socks is 0.5. Compare youranswer to those in (a).
