Question

6) Transmissions for a given model of car are built in 3 different factories. It is determined that: . Factory A produces 32% of the transmissions used, and 1 in 178 are defective. . Factory B produces 41% of the transmissions used, and 1 in 220 are defective. . Factory C produces 27% of the transmissions used, and l in 204 are defective. If a randomly selected car has a defective transmission, what is the probability the transmission was built in factory B?

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Answer #1

P(defective transmission)=P(factory A and defective transmission)+P(factory A and defective transmission)+P(factory A and defective transmission) =0.32*(1/178)+0.41*(1/220)+0.27*(1/204)

=0.004985

therefore P(factory B given defective)=0.41*(1/220)/0.004985 =0.373855 ~ 0.3739

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