Question

The GMC Acadia is a sports utility vehicle that comes in only Regular and Denali (or deluxe) models. Assume that for the 2019 version, 40% of the Acadias sold were Regular models. Of those buying the Regular model, 30% purchase an extended warranty, whereas 50% of all Denali purchasers do so. If you learn that a randomly selected Acadia purchaser has an extended warranty, how likely is it that he or she has a Regular model?

Answer 1

Here we need to find, if we know the randomly selected Acadia purchaser has an extended warranty, how likely is it that he or she has a Regular model

i.e. P(Regular model / purchaser has an extended warranty)

= P(Regular model and purchaser has an extended warranty) / P(purchaser has an extended warranty) --> A)

Now,

P(Regular model and purchaser has an extended warranty) = 0.40*0.30 = 0.12 --> i)

P(purchaser has an extended warranty)

= P(Regular model and purchaser has an extended warranty) + P(Denali model and purchaser has an extended warranty)

= 0.40*0.30 + (1-0.40)*0.50

= 0.42 --> ii)

Putting i) and ii) in A), we get

Require probability = 0.12/0.42

= 0.2857