A market study taken at a local sporting goods store showed that of 30 people qu

Question

A market study taken at a local sporting goods store showed that of 30 people questioned, 18 owned tents, 15 owned sleeping bags, 14 owned camping stoves, 6 owned both tents and camping stoves, and 10 owned both sleeping bags and camping stoves: What is the probability of owning a tent, owning a camping stove, owning a sleeping bag, owning both a tent and a camping stove, and owning both a sleeping bag and a camping stove? What is the probability of owning a tent or a camping stove? What is the probability of owning neither a camping stove or a tent Given a person questioned owns a tent, what is the probability he also owns a camping stove? Are the events of owning a tent and owning a camping stove mutually exclusive? Explain briefly? Are the events of owning a sleeping bag and owning a camping stove independent? Explain Briefly? If four people questioned owned a tent, a sleeping bag, and a camping stove, then up to how many can own only a camping stove?

Explanation / Answer

P(T) = 18/30 = 0.6

P(CS) = 14/30

P(SB) = 15/30 = 0.5

P (T + CS) = 6/30 = 0.2

P(CS + SB) = 10/ 30 = 0.333

.

P( T or CS) = P(T) + P(CS) - P(T + CS) = 18 + 14 - 6 = 26 / 30

P ( No CS or tent) = 1 - 26/30 = 4/30

.

P(CS | T) = 6 / 18 = 1/3

No the events of owing a tent and camping stove are not exclusive, because

P(CS + T) is not zero.

.

Similar to above arguement, P (CS + SB) is not zero.Hence, they are not mutually exclusive.

.

If 4 people own all three equiment, then number of people owning only camping stove

P(CS only) = P(CS) - P(CS+SB) - P(CS+T) + P(CS + T + SB)

= 14 - 10 - 6 + 4

= 2 people can own only a camping stove and nothing more

Hope this helps.

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