Question

A manufacturing company produces parts that are good (90%), partially defective (2%), or completely defective (8%). These parts pass through an automatic inspection machine, which is able to detect and discard any part that is completely defective. What is the probability that a part is good given that it 4 passed the inspection machine

Answer 1

The probability that a part is good given that it passed the inspection machine is P=0.978.

Explanation:

As the inspection machine detect and discard any part that is completely defective, only the good and partially defective parts passed this inspection.

Then, if we have:

Probability of being a good part P(G)=0.90

Probability of being a patially defective part P(P)=0.02

Probability of being a completely defective part P(D)=0.08.

Probability of passing the inspection machine = 1-P(D)=1-0.08=0.92

Then, the probability of having a good part, given that it passed the inspection machine is:

`P(G|Pass)=P(G)/P(Pass)=0.90/0.92=0.978`