ITPEC FE Morning October 2020 Question 3

Source exam: ITPEC FE Morning October 2020Topic: Basic Theory & Math

ITPEC FE Morning October 2020 — Question 3 of 80

Bayes' Theorem (conditional probability) — find which source is more likely given a known outcome.

Given:
- Line A: 60% of production, 2% defect rate

- Line B: 40% of production, 1% defect rate

- A defective product is found — what is the probability it came from Line A?

Step-by-step:
- P(defect from A) = 0.60 × 0.02 = 0.012

- P(defect from B) = 0.40 × 0.01 = 0.004

- P(defect total) = 0.012 + 0.004 = 0.016

- P(A | defect) = 0.012 / 0.016 = 0.7575%

Why not others:
- (a) 40 — incorrectly compares defect rates without weighting by production share

- (b) 50 — would apply only if both lines had equal share and equal defect rates

- (c) 60 — production share of Line A alone, ignoring different defect rates

Key formula: P(A|D) = P(D|A) × P(A) / [P(D|A) × P(A) + P(D|B) × P(B)]

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