A relay assembly line receives 65 percent of its relays from supplier X and 35 percent from supplier Y. Relays from supplier X are defective at a rate of 2.0 percent, and relays from supplier Y are defective at a rate of 5.0 percent. A relay drawn at random from stock fails incoming inspection. The probability that the failed relay came from supplier X is most nearly:
- (A)0.286
- (B)0.426
- (C)0.574
- (D)0.714
Show worked solution
Answer: (B)
Weighting each supplier's defect rate by its share leaves supplier X responsible for 0.0130 of the 0.0305 total defect probability, about 43 percent of all defective relays.
Supplier share and supplier-specific defect rate combine into the unconditional defect probability that serves as the denominator of the reverse conditional.
Bayes' theorem rescales the single branch belonging to supplier X against that total.
FE Reference Handbook — Engineering Probability and Statistics: Bayes' Theorem
Why the other choices appear
- (A)0.286 comes from normalizing the two defect rates alone, 0.020/(0.020+0.050), discarding the 65/35 supply shares.
- (C)0.574 is 0.0175/0.0305, the posterior probability for supplier Y, obtained by inverting the wrong branch.
- (D)0.714 is 0.050/(0.020+0.050), combining both errors: unweighted defect rates and the wrong supplier.