statistics
posted by Sam on .
Use Bayes' theorem to solve this problem. A storeowner purchases stereos from two companies. From Company A, 150 stereos are purchased and 7% are found to be defective. From Company B, 900 stereos are purchased and 9% are found to be defective. Given that a stereo is defective, find the probability that it came from Company A.
Is the answer 7/61 = .11475?

Of the defective stereos on hand, 10.5 were probably from A and 81 probably from B.
10.5/91.5 are from A. That equals 7/61.
To get the answer with Bayes' theorem,
P(yx) = P(xy)*P(y)/P(x)
P(x) = probability it is defective regardless of source = 91.5/1050
P(y) = probability it is from A, defective or not = 150/1050
P(xy) = probability that it is defective, if from A = 0.07
P(yx) = probability it is from A, if defective
= .07* (150/91.5) = .11475..