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

Answer:

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

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

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.

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.015}{0.06} = 0.25$

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