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AleksAgata [21]
3 years ago
15

A particular electronic component is produced at two plants for an electronics manufacturer. Plant A produces 70% of the compone

nts used and the remainder are produced by plant B. Among the components produced at plant A, the proportion of defective components is 1%. Among the components produced at plant B, the proportion of defective components is 2%. If a component received by the manufacturer is defective, the probability that it was produced at plant A is
Mathematics
1 answer:
Vesna [10]3 years ago
4 0

Answer:

If a component received by the manufacturer is defective, the probability that it was produced at plant A is 0.5385 = 53.85%.

Step-by-step explanation:

We use the Bayes Theorem to solve this question.

Bayes Theorem:

Two events, A and B.

P(B|A) = \frac{P(B)*P(A|B)}{P(A)}

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Defective component

Event B: Produced at plant A.

Plant A produces 70% of the components used

This means that P(B) = 0.7

Among the components produced at plant A, the proportion of defective components is 1%.

This means that P(A|B) = 0.01

Probability of a defective component:

1% of 70%(defective at plant A)

2% of 100 - 70 = 30%(defective at plant B). So

P(A) = 0.01*0.7 + 0.02*0.3 = 0.013

If a component received by the manufacturer is defective, the probability that it was produced at plant A is

P(B|A) = \frac{0.7*0.01}{0.013} = 0.5385

If a component received by the manufacturer is defective, the probability that it was produced at plant A is 0.5385 = 53.85%.

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