4. For this problem, you’ll compare the hypergeometric and binomial distributions. Suppose there is a sock...

4. For this problem, you’ll 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.

(a) 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:

(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’t make much sense if you are planning to wear the socks!). Calculate the probability of getting at least two black socks when you sample four socks and the proportion of black socks is 0.5. Compare your answer to those in (a).

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Expert Solution

milcah answered 4 months ago

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