Question

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.

Answer 1

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%