Reconsider the previous exercise.

Previous exercise: A college professor was assigned to a committee of six people, composed of four men and two women. The committee selected two officers to carry out the majority of its administrative work, and both of the women were selected. The professor wondered whether or not this constituted evidence of subtle discrimination, so she considered how unlikely such an event would be if the two officers had been chosen at random from the six committee members.

d. If the process of randomly selecting two people from among these six people were repeated over and over, in the long run what percentage of the time would two men be selected as officers? Would such an outcome be a surprising result using random selection?

e. Repeat part d for the outcome of one man and one woman.

f. If the two officers were chosen at random, what would be the most likely gender breakdown, two men, two women, or one of each?

g. Use the sample space in part a to calculate the theoretical expected number of men among the two officers. How close did your simulated estimate come to the theoretical expected value?