A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 30% of the cameras sold have been of the basic model. Of those buying the basic model, 44% purchase an extended warranty, whereas 40% 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?

the probability is 0.32 (32%)

Step-by-step explanation:

defining the event W = has extended warranty, then

P (W) = probability of purchasing the basic model * probability of purchasing extended warranty given that has purchased the basic model + probability of purchasing the deluxe model * probability of purchasing extended warranty given that has purchased the deluxe model = 0.3 * 0.44 + 0.7 * 0.40 = 0.412

then using the theorem of Bayes for conditional probability and defining the event B = has the basic model, then

P (B/W) = P (B∩W) / P (W) = 0.3 * 0.44/0.412 = 0.32 (32%)

where

P (B∩W) = probability of purchasing the basic model and purchasing the extended warranty

P (B/W) = probability of purchasing the basic model given that has purchased the extended warranty