Calculators produced by a manufacturer were of poor quality and 300 shipments we

Question

Calculators produced by a manufacturer were of poor quality and 300 shipments were sent with 40% defective. After tightening up quality control, this figure was reduced to 10% defective. 900 shipments were sent. Amazon wanted to know whether a shpment was produced before or after quality control. A) before opening a shipment and testing the calculators, what was the chance it was one of the poor ones? b) the shipment was opened, and a calculator tested. it was defective. now what is the chance it was one of the poor shipments? Please explain your answer, thanks!

Explanation / Answer

(a) Prob = (300*0.4 + 900*0.1)/1200 = 0.175

(b) P(P | def) = [P(def | P)(P(P) ] /[P(def | P)(P(P) + P(def | T)(P(T) ]

= 0.4*(300/1200)/[0.4*(300/1200) + 0.1*(900/1200)]

= 0.4/(0.4+0.3) = 4/7

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