Probability... A company that manufactures video camera produces a basic and deluxe model, over the past year?

Question

A company that manufactures video camera produces a basic and deluxe model, over the past year 40% of the cameras sold have been of the basic model. Of those buying the basic model 30% purchase an extended warranty, whereas 50% of all deluxe purchasers do so.

If you learn that a radomly selected purchaser has an extended warranty how likely is it that he or she has a basic model?

My Answer: .286 or 28.6%

I got that using his..

P(B | A) = P(B and A)/ P(A)

for

B=has basic model

A=has extendd warranty

so .12/.42=.286

is this right?

Answer 1

Looks right to me.

W = extended warranty

B = basic model

D = deluxe model

P(W) = P(B and W) + P(D and W) = 0.4*0.3+0.6*0.5 =0.42

P(B|W)  = P(B and W) / P(W) = 0.12/0.42