FE Mechanical Probability and Statistics Practice Problems

The current FE Mechanical specification assigns 4-6 of the 110 exam questions to Probability and Statistics. Form A contains 5 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A bearing assembly line draws 65 percent of its bearings from supplier A and 35 percent from supplier B. Supplier A ships 2.0 percent defective units; supplier B ships 5.0 percent defective units. A bearing drawn at random from the line is found to be defective. The probability that it came from supplier B is most nearly:

(A)0.350
(B)0.426
(C)0.574
(D)0.714

Show worked solution

Answer: (C)

Supplier B ships the smaller volume but the higher defect rate, and weighting each rate by its production share assigns about 57 percent of the defective bearings to supplier B.

Defective units arise from two mutually exclusive supplier streams, so the overall defect rate is the share-weighted sum of the two individual rates.

P (D) = P (A) P (D ∣ A) + P (B) P (D ∣ B) = 0.65 (0.020) + 0.35 (0.050) = 0.0305

Reversing the direction of conditioning divides supplier B's joint contribution by that overall rate.

P (B ∣ D) = \frac{P ( B ) P ( D ∣ B )}{P ( D )} = \frac{0.0175}{0.0305} = 0.574

FE Reference Handbook — Engineering Probability and Statistics: Bayes' Theorem

Why the other choices appear

(A)Reports the prior production share P(B) = 0.350 without updating on the observed defect.
(B)Computes the complementary posterior P(A|D) = 0.0130/0.0305 = 0.426, the wrong supplier.
(D)Forms the ratio of defect rates alone, 0.050/(0.020 + 0.050) = 0.714, omitting the production shares.