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ESI 6321
APPLIED PROBABILITY METHODS IN ENGINEERING
OEM 2009
January 12, 2008
QUIZ + SOLUTIONS
8:009:00AM
Open book
This quiz consists of 3 problems
Name:
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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(BA)=0.10 and P(BA’)=1. We are interested
in finding P(B). This probability is equal to P(B) = P(BA)P(A) + P(BA’)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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 Spring '07
 JosephGeunes

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