Allied & ICAR Exam Bank • ALLIED_1029 NAT • 2 Marks

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Bayes' theorem

Question Statement:

A diagnostic sensor detects a faulty bearing correctly 95% of the time, and gives a false positive for a healthy bearing 5% of the time. If 2% of bearings are truly faulty, the probability that a bearing flagged as faulty is ACTUALLY faulty is:

Answer Key:

0.279

Step-by-Step Solution & Explanation

By Bayes' theorem: $P(F|+) = \frac{P(+|F)P(F)}{P(+|F)P(F) + P(+|H)P(H)} = \frac{0.95 \times 0.02}{(0.95 \times 0.02) + (0.05 \times 0.98)} = \frac{0.019}{0.019 + 0.049} = \frac{0.019}{0.068} \approx 0.2794$.
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