A Market Study Taken at a Local Sporting Goods Store

Essay

A market study taken at a local sporting goods store showed that of 20 people questioned, 6 owned tents, 10 owned sleeping bags, 8 owned camping stoves, 4 owned both tents and camping stoves, and 4 owned both sleeping bags and camping stoves. Let Event A = owns a tent, Event B = owns a sleeping bag, Event C = owns a camping stove, and Sample Space = 20 people questioned.
a. Find P(A), P(B), P(C), P(AC), P(BC).
b. Are the events A and C mutually exclusive? Explain briefly.
c. Are the events B and C independent events? Explain briefly.
d. If a person questioned owns a tent, what is the probability he also owns a camping stove?
e. If two people questioned own a tent, a sleeping bag, and a camping stove, how many own only a camping stove?
f. Is it possible for 3 people to own both a tent and a sleeping bag, but not a camping stove?