An automobile plant contracted to buy shock absorbers from t

An automobile plant contracted to buy shock absorbers from two local suppliers, Bolt & Co. and Acme, Inc. Bolt supplies 40% and Acme 60%. All shocks are subject to quality control. The ones that pass are called reliable.

Of Acme’s shocks, 90% test reliable. But Bolt has been having some problems on the line, and recently only 70% of Bolt’s shock absorbers have tested reliable. What is the chance that a randomly chosen shock absorber, which is tested and found to be reliable, is made by Bolt? Show your work.

Solution

Let

A = acme
B = bolt
R = reliable

Hence,

P(R) = P(A) P(R|A) + P(B) P(R|B)

P(R) = 0.60*0.90 + 0.40*0.70 = 0.82

Thus,

P(B|R) = P(B) P(R|B) / P(R) = 0.40*0.70/0.82 = 0.341463415 [ANSWER]