Question: Need help with the questions below. Please use the same alphabet when answering the questions to prevent confusion. Thanks 7. (20 points) There are three

Need help with the questions below. Please use the same alphabet when answering the questions to prevent confusion. Thanks

7. (20 points) There are three machines that produce pencils in my factory.Machine A produces defective pencils 3% of the time, machine B produces defective pencils 6% of the time, and machine C produces defective pencils 14% of the time. Of the total output from these machines, 80% of the produced pencils are from machine A, 16% are from machine B, and only 4% are from machine C.One pencil is chosen at random from the daily production.

a. What is the prior probability that the pencil came from machine A?

b. What is the prior probability that the pencil came from machine B?

c. What is the prior probability that the pencil came from machine C?

d. If, upon inspection, the pencil is found to be defective, what is the revised probability that it came from machine A?

e.If, upon inspection, the pencil is found to be not defective, what is the revised probability that it came from machine B?

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