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3. (3 marks) (fron P. 32 #61) Suppose that chips for an integrated circuit are tested and that the probability that they are detected if they are defective is .95 and the probability that they are declared sound if in fact they are sound is .97. If .5% of the chips are faulty, what is the probability that a chip that is declared sound is sound?
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Answer #1

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P(chip declared sound, is sound) =

p(chip sound)*p(chip sound, is declared sound) / p(chip not sound)*P(chip not sound but declared sound ) + p(chip sound)*p(chip sound, is declared sound)

= .995*.97 / (.995*.97 + .005*(1-.95))

= 0.99974

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