ITPEC FE Morning October 2018 Question 3
ITPEC FE Morning October 2018 — Question 3 of 80
Bayes' Theorem (conditional probability) — given that a defect was found, determine which source most likely produced it.
We apply Bayes' theorem: P(A | defective) = P(defective | A) × P(A) / P(defective).
Given:
- Line A produces 60% of products with a 2% defective rate
- Line B produces 40% of products with a 1% defective rate
Step-by-step:
1. P(defective from A) = 0.60 × 0.02 = 0.012
2. P(defective from B) = 0.40 × 0.01 = 0.004
3. P(defective total) = 0.012 + 0.004 = 0.016
4. P(A | defective) = 0.012 / 0.016 = 0.75 = 75%
Why not others:
- (a) 40 — this is the share of defects from line B (0.004 / 0.016), not A
- (b) 50 — incorrectly assumes equal contribution from both lines
- (c) 60 — uses the raw production share of A without applying the defective rate
Key rule: Bayes' theorem adjusts prior probability (production share) using new evidence (defect rates) — multiply share × defect rate for each source, then divide by the total.
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