A manufacturing process produces integrated circuit chips. Over the long run, the fraction of bad chips produced by the process is 20%. Thoroughly testing a chip to determine whether it is good or bad is rather expensive, so a cheaper test is used. All good chips will past the test, but so will 7.5% of the bad chips. (a) Given that a chip passes the test, what is the probability that it is a good chip? Use at least 3 decimal places. (b) If the company sells all chips that pass the cheaper test, what percentage of sold chips will be bad? Use at least 3 decimal places.

(a) Given that a chip passes the test, what is the probability that it is a good chip?

LetB = {the chip is good}

A={the chip passes the cheap test}.

Bc={the chip is bad}

Ac={the chip fails the cheap test}

P(A | B) = 1

P(A | B c ) = 0.075

= =  ≈ 0.9751

(b) If the company sells all chips that pass the cheaper test, what percentage of sold chips will be bad?

P(B c  |A) =  1 − P(B | A) = 1 -  0.9751 = 0.0249

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