A store-owner purchases stereos from two companies. from company a, 450 stereos are purchased and 6% are found to be defective. from company b, 550 stereos are purchased and 4% are found to be defective. given that a stereo is defective, find the probability that it came from company

a. enter your answer as a percent, rounded to the nearest tenth of a percent.

Bayes’ theorem P (P|Q) = P (P∩Q) / P (Q) = P (Q∩P) / P (Q) = P (Q∩P) / P (P) * (P (P) / P (Q)) = P (Q|P) * (P (P) / P (Q)) Or just:P (P|Q) = P (Q|P) * (P (P) / P (Q))

Company A: 6% x 450 = 27 are bad

Company B: 4% x 550 = 22 are bad

Total bad of defective stereos = 27 + 22 = 49

P (A | Bad) = 27 / 49 = 0.5510

So Probability that the defective one is from A = 0.5510 or 55.10%