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Dr. Edwin Romeijn
ESI 6321 Applied Probability Methods in Engineering
Practice Problem Set  Solutions
Class of 2009

7

ESI 6321 APPLIED PROBABILITY METHODS IN ENGINEERING
OUTREACH ENGINEERING MANAGEMENT
Class of 2009
PRACTICE PROBLEM SET  SOLUTIONS
Exercise 2.3
(a) P(At least 4 years experience) = P(4 years experience) + P(5 or more years
experience) = 15/100 + 35/100 = 50/100.
(b) P(At least 4 years experience  At least 3 years experience) = P(At least 4 years
experience)/P(At least 3 years experience) = (50/100)/(80/100) = 50/80.
Exercise 2.9
Let H
+
denote the event that the person is infected with HIV and H
–
that the person is
not infected. Furthermore, let R denote the event that the test is positive and N that the
test is negative. Then it is given that P(H
+
) = 550,000/250,000,000 = 0.0022, P(R  H
+
)
= 0.99, and P(N  H
–
) = 0.99.
(a) We want to compute P(H
+
 R). Notice that
P(R) = P(R  H
+
) x P(H
+
) + P(R  H
–
) x P(H
–
) =
= 0.99 x 0.0022 + 0.01 x (10.0022) = 0.002178 + 0.009978 = 0.012156.
Therefore, P(H
+
 R) = P(R  H
+
) x P(H
+
)/P(R) = 0.002178/0.012156 = 0.18.
(b) Let D denote the event that the person is a drug user. We want to compute P(H
+
 R
and D).
Note that P(H
+
and D) = 275,000/250,000,000 = 0.0011 and P(H
–
and D) =
(10,000,000 – 275,000)/250,000,000 = 0.0389.
We assume that P(R  H
+
and D) = P(R  H
+
) = 0.99 and P(N  H
–
and D) = P(N  H
–
)
= 0.99. That is, drug using doesn’t influence the test accuracy.
Then P(R
∩
D) = P(R  H
+
and D) x P(H
+
and D) + P(R  H
–
and D) x P(H
–
and D) =
= P(R  H
+
and D) x P(H
+
and D) + (1  P(N  H
–
and D)) x P(H
–
and D) =
= (0.99) x (0.0011) + (1  0.99) x (0.0389) = 0.001478.
Therefore, P(H
+
 R and D) = P(H
+
and R and D)/P(R and D) =
= P(R  H
+
and D) x P(H
+
and D)/P(H
+
and D)
= (0.99) x (0.0011)/(0.001478) = 0.74.
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View Full DocumentDr. Edwin Romeijn
ESI 6321 Applied Probability Methods in Engineering
Practice Problem Set  Solutions
Class of 2009

8

Exercise 2.14
(a) Let the random variable
A
denote the time to complete Task A,
B
denote the time
to complete Task B, and
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 Spring '07
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