A company sells two types of video cameras-a basic model anda deluxe model. Over

Question

A company sells two types of video cameras-a basic model anda deluxe model. Over the past year, 40% of the cameras sold werethe basic model and 60% were the deluxe model. Of those who boughtthe basic model, 30% purchased an extended warranty, whereas 60% ofthose who bought the deluxe model purchased an extendedwarranty.

a) if you learn that a randomly selected customer bought anextended warranty, what is the probability that this personpurchased a basic model?
b) what is the probability that a randomly chosen customer boughtan extended warranty?

Explanation / Answer

P(basic) = 0.40, P(deluxe) = 0.60 P(ew|basic) = 0.30, P(ew|deluxe) = 0.60 a) P(basic|ew) = P(basic and ew)/P(ew) = P(basic)*P(ew|Basic)/[P(basic)*P(ew|basic) +P(deluxe)*P(ew|deluxe)] = 0.40*0.30/[0.40*0.30+0.60*0.60] = 0.25 b) P(ew) = P(basic)*P(ew|basic) + P(deluxe)*P(ew|deluxe) = 0.40*0.30+0.60*0.60 = 0.48

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