1. A campus club has 400 members. Of these, 100 live in a dorm room and 300 do not. 0f the 100 who live in a dorm room, 90 have a campus meal plan. Of the 300 who do not live in a dorm room, 60 have a campus meal plan. We choose a single club member at random from among the 400 members. Let A be the event that the club member lives in a dorm room, and let B be the event that the club member has a campus meal plan. (a) Are A and B mutually exclusive? Explain why or why not. (b) Are A and B independent? Explain why or why not