A Bluetooth earphone produced by the Fisher Corporation was found to be defectiv

Question

A Bluetooth earphone produced by the Fisher Corporation was found to be defective (D). There are three facilities (A, B, C) where such earphones are manufactured. A Quality Control Manager (QCM) is responsible for investigating the source of found defects. This is what the QCM knows about the company's earphone production and the possible source of defects:

If a randomly selected earphone is defective, what is the probability it was manufactured at facility C?

Hint: P(D) = P(D and A) or P(D and B) or P(D and C). Now you need to do a slight converstion of each of those terms using what you learned about conditional probabilities.

Note: For full credit, use Bayes’s Theorem and show all of your logic.

Facility % of total production Probability of defective earphone A 0.40 0.020 B 0.35 0.025 C 0.25 0.015

Explanation / Answer

probabilty of defective =P(D)=P(A)*P(D|A)+P(B)*P(D|B)+P(C)*P(D|C)

=0.4*0.02+0.35*0.025+0.25*0.015=0.0205

hence  probability it was manufactured at facility C; given defective =P(C|D)=P(C)*P(D|C)/P(D)=0.25*0.015/0.0205

=0.182927

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