3. Faculty Promotions
Among ten faculty members considered for promotions at Random U., there are six men and four women. It has already been decided (perhaps for budgetary reasons) that exactly two faculty members will receive promotions. In keeping with tradition at Random U., all faculty members are equally likely to receive promotions.
(a) What is the probability distribution for the number of women faculty promoted at Random U.?
(Remember, a probability distribution lists each possible value of the random variable with its corresponding probability). Hint: Draw a tree. The first branch is W1/M1 (first member chosen is a woman/first member chosen is a man).
(b) What are the possible values for the number of women promoted? What are the mean, variance, and standard deviation of the random variable, the number of women faculty promoted at Random U.?
