We produce automobile tires. We have two production facilities, Buffalo and Alba

Question

We produce automobile tires.
We have two production facilities, Buffalo and Albany.
Although Buffalo produces 60% of our tires, only 2% (.02) ofBuffalo's tires have a slight blemish when they reach the retailstores.
0.16 of Albany's tires have a blemish.
The blemish does not affect safety and the tires are sold at fullprice.
Assuing independence in the delivery system (as opposed to Albanyshipping near Albany and likewise Buffalo), if you visit a retailerin Syracuse and inspect a tire and fiind a blemish, what is theprobability it was manufactured in Buffalo?

Decimal answer, to 3 decimal places.

Explanation / Answer

Let B= Buffalo produced    b=Blemish   and A= Albany produced We are given P(B)=.6 therefore P(A)=.4 P(b/B)=.02 P(b/A)=.16 Now we want to find P(B/b)=P(Bnb)/P(b) =P(b/B)P(B)/P(b) We need P(b)=P(bnB) + P(bnA) = P(b/B)P(B)+P(b/A)P(A)=.02(.6)+.16(.4)=.076 Therefore, P(B/b)=.02(.6)/.076=.158

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