From 10 men and 8 women in a pool of potential jurors, 12 are chosen at random to constitute a jury. Suppose that you observe the number of men who are chosen for the jury. Let A be the event that at least half of the 12 jurors are men, and let B be the event that at least half of the 8 women are on the jury.
a. Determine the sample space for this experiment.
b. Find (A or B), (A & B), and (A & (not B)), listing all the outcomes for each of those three events.
c. Are events A and B mutually exclusive? Are events A and (not B)? Are events (not A) and (not B)? Explain.