From 10 men and 8 women in a pool of potential jurors, 12 people are chosen at random to constitute a jury. Suppose that you observe the number of men who are chose for the jury. Let A be the event that at least half of the 12 jurors are men and B be the event that at least half of the 8 women are on the jury.

(a) Determine the sample space of this random experiment.
(b) Find A B, A B, and A B? listing the outcomes for each of those three events.
(c) Are A and B mutually exclusive? (explain your answer) (d) Are A and B? mutually exclusive?(explain your answer)
(e) Are A? and B? mutually exclusive?(explain your answer