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

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%.

123

step-by-step explanation:

agngel

256π units²   (answer b)

step-by-step explanation:

the formula for the surface area of a sphere of radius r

is             a = 4πr²

and so, if r = 8 units, then the surface area is:

a = 4π(8 units)² = 256π units²   (answer b)