Exercise · ZW-BAYES-THEOREM-005 · ★★☆ Intermediate

Three machines make 50 %, 30 % and 20 % of the parts, with 1 %, 2 % and 5 % defective. A part is found defective. What is the probability it came from machine 1?

Choose one option.

Show answer

D. 5/21

Explanation

\(\dfrac{0.005}{0.021}=\dfrac5{21}\). Though machine 1 makes half the parts, it is the least defective.

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Review the concept: Bayes' theorem

Bayes' theorem inverts a conditional probability: it gives the probability \(P(B_j\mid A)\) of a cause \(B_j\) given an observed effect \(A\), from the probability of the effect given that cause.

\[P(B_j\mid A)=\frac{P(A\mid B_j)\,P(B_j)}{\sum_{i}P(A\mid B_i)\,P(B_i)}\]

More practice problems: bayes' theorem

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