alleryIn a factory, 60% of items come from Machine A and 40% from Machine B. 2% of A-items and 5% of B-items are defective. P(item from B | defective) is closest to
A0.60
B0.36
C0.63
D0.40
Answer & Solution
Correct answer: C. 0.63
1. P(A) = 0.6, P(B) = 0.4. P(D|A) = 0.02, P(D|B) = 0.05.
2. Total P(D) = 0.6 × 0.02 + 0.4 × 0.05 = 0.012 + 0.020 = 0.032.
3. P(B|D) = P(B) P(D|B) / P(D) = 0.020 / 0.032.
4. = 0.625, i.e. about 0.63.
_Source: syllabus Mathematics, Ch 13 "Probability", §13.5_
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