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# Quiz1Solutions - ESI 6321 APPLIED PROBABILITY METHODS IN...

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1 ESI 6321 APPLIED PROBABILITY METHODS IN ENGINEERING OEM 2009 January 12, 2008 QUIZ + SOLUTIONS 8:00-9:00AM Open book This quiz consists of 3 problems Name:

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2 Problem 1: (30 points) Suppose that a fraction 5% of the microchips produced by a leading microchip manufacturer is defective. Historically, given that a microchip is defective, the inspector (wrongly) accepts the chip 10% of the time, thinking it has no defect. If a microchip is not defective, he always correctly accepts it. (a) What is the probability that the inspector accepts a particular microchip? Let A denote the event that the microchip is defective (and thus A’ the event that it is not defective) and let B denote the event that the microchip is accepted (and thus B’ the event that the microchips is not accepted). We know that P(A)=0.05 and P(A’)=0.95. Moreover, we know that P(B|A)=0.10 and P(B|A’)=1. We are interested in finding P(B). This probability is equal to P(B) = P(B|A)P(A) + P(B|A’)P(A’) = 0.10 × 0.05 +1 0.95 = 95.5%. (b) Given that the inspector accepts a microchip, what is the probability that it has no defect? (If you were unable to answer (a), please denote the answer to (a) by p ) . Using the same events as in (b), we are interested in finding P(A’|B). This probability
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Quiz1Solutions - ESI 6321 APPLIED PROBABILITY METHODS IN...

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