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 events A and C mutually exclusive? Explain briefly.
c. Are 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 three people to own both a tent and a sleeping bag, but not a camping stove?
a. P(A) = .3, P(B) = .5, P(C) = .4, P(A?C) = .2, P(B?C) = .2
b. not mutually exclusive; there are four people who own both a tent and stove
c. independent
d. P(C | A) = .667
e. two people own only a stove
f. no
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