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

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

Step-by-step explanation:

Conditional Probability

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

In which

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

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

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

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

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

a

step-by-step explanation: