Question

A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 46% of the cameras sold have been of the basic model. Of those buying the basic model, 34% 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

Let B be the event that cameras sold are of basic model and D be the event that cameras sold are of deluxe model. W be the event that purchaser has an extended warranty. then the problem can be solved using the Bayes' theorem. Given that

P(B) = 0.46, P(D) = 1- P(B) = 0.54,

P(W|B) = 0.34, P(W|D) = 0.47. Then,

P( purchaser buys a basic model given that he/she has an extended warranty ) = P(B|W)