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A company has two machines that produce widgets. An older machine produces 20% defective widgets, while...

A company has two machines that produce widgets. An older machine produces 20% defective widgets, while the new machine produces only 3% defective widgets. However, the older machine produces 8 times as many widgets as the new machine does. What is the probability that a randomly chosen widget produced by the company is both produced by the new machine and is defective? Answer is 0.0033

math   Statistics-And-Probability   
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Answer #1

Let p be the probability that a part is produced in new machine

P(a part is produced in old machine) = 8p

P(a part is produced in old machine) + P(a part is produced in new machine) = 1

8p + p = 1

p = 1/9

P(a part produced in new machine is defective) = 0.03

P(a randomly chosen widget produced by the company is both produced by the new machine and is defective) = P(a part is produced in new machine) x P(a part produced in new machine is defective)

= 1/9 x 0.03

= 0.0033

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