A company that manufactures video cameras produces only a basic model and a delu

Question

A company that manufactures video cameras produces only a basic model and a deluxe model. Over the past year, 70% of the cameras sold have been of the basic model. Of those buying the basic model, 25% purchase an extended warranty, while 55% of purchasers of the deluxe model will purchase an extended warranty. (a) If learn that a customer has purchased an extended warranty, what is the probability that he or she has a basic model camera? (b) Are purchasing a basic model and purchasing an extended warranty disjoint events? Explain using a probability argument. (c) Are purchasing a model and purchasing an extended warranty basic independent events? Explain using a probability argument.

Explanation / Answer

P(basic model camera) = 0.7

P(delux model camera) = 1 - 0.7 = 0.3

P(extended warranty | basic model camera) = 0.25

P(extended warranty | delux model camera) = 0.55

a) P(extended warranty) = P(extended warranty | basic model camera) * P(basic model camera) + P(extended warranty | delux model camera) * P(delux model camera)

= 0.25 * 0.7 + 0.55 * 0.3

= 0.34

P(extended warranty | basic model camera) =  P(extended warranty | basic model camera) * P(basic model camera) /  P(extended warranty)

= 0.25 * 0.7 / 0.34

= 0.51

b) No, Basic model camera and purchasing an extended warranty are not disjoint events. Because, P(Basic model camera and purchasing an extended warranty) not zero.

c) No, Basic model camera and purchasing an extended warranty are not independent events. Because,

P(extended warranty | basic model camera) is not equal to P(extended warranty)

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