An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable. Of Y’s shock absorbers, 72% are reliable.
The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is
Probability that the absorber is reliable = 0.96*0.6 + 0.72*0.4 = 0.576 + 0.288 Probability that the absorber is from y and reliable = (Probability that is made by Y) X (Probability that it is reliable) = 0.4 * 0.72 = 0.288 The probability that randomly picked reliable absorber is from y = (Probability that the absorber is from y and reliable) / (>Probability that the absorber is reliable ) = (0.288)/ (0.576 + 0.288) = 0.334