Question

A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 47% of the cameras sold have been of the basic model. Of those buying the basic model, 39% purchase an extended warranty, whereas 47% of all deluxe purchasers do so. If you learn that a randomly selected purchaser has an extended warranty, how likely is it that he or she has a basic model? (Round your answer to four decimal places.)

Answer 1

P(basic model) = 0.47

P(deluxe model) = 1 - 0.47 = 0.53

P(purchase an extend warranty | basic model) = 0.39

P(purchase an extend warranty | deluxe model) = 0.47

P(purchase an extend warranty) = P(purchase an extend warranty | basic model) * P(basic model) + P(purchase an extend warranty | deluxe model) * P(deluxe model)

= 0.39 * 0.47 + 0.47 * 0.53

= 0.4324

P(basic model | purchase an extend warranty) = P(purchase an extend warranty | basic model) * P(basic model) / P(purchase an extended warranty)

= 0.39 * 0.47 / 0.4324

= 0.4239