Question

Half of a set of the parts are manufactured by machine A and half by machine B. Six percent of all the parts are defective. Three percent of the parts manufactured on machine Are defective. Find the probability that a part was manufactured on machine A, given that the part is defective. (Round your answer to 4 decimal places.) Probability

Answer 1

0.25 = 25% probability that a part was manufactured on machine A, given that the part is defective.

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Defective

Event B: Manufactured by machine A.

Six percent of all the parts are defective.

This means that
`P(A) = 0.06`

Probability that a part is defective and was manufactured on machine A

3% of the parts manufactured on machine A are defective, manufacture A is responsible for 50% of the parts. So

`P(A \cap B) = 0.03*0.5 = 0.015`

Find the probability that a part was manufactured on machine A, given that the part is defective.

`P(B|A) = (P(A \cap B))/(P(A)) = (0.015)/(0.06) = 0.25`

0.25 = 25% probability that a part was manufactured on machine A, given that the part is defective.