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.
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
Among the components produced at plant A, the proportion of defective components is 1%.
This means that
Probability of a defective component:
1% of 70%(defective at plant A)
2% of 100 - 70 = 30%(defective at plant B). So
If a component received by the manufacturer is defective, the probability that it was produced at plant A is
If a component received by the manufacturer is defective, the probability that it was produced at plant A is 0.5385 = 53.85%.