Question

Cases in Probability

A Bayes Theorem Case

Three manufacturing processes, A, B and C, produce wheel bearings. Proportions of the bearings produced by the processes are: 60%, 30% and 10%, respectively. Expected percentages of defective bearing manufactured by the processes are 2%, 3% and 5%, respectively.

Wheel Bearing

An inspection has randomly selected a defectivebearing. What is the probability that the bearing was produced by process Bqmarkgreen.gif

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Answer #1

P(defective)=P(from A and defective)+P(from B and defective)+P(from C and defective)

=0.6*0.02+0.3*0.03+0.1*0.05=0.026

hence P(from process B given defective)

=P(from B and defective)/P(defective)=0.3*0.03/0.026=0.346154

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