King Fahd University of Petroleum & Minerals
Department of Mathematics & Statistics
STAT-319-Term081-Quiz2A-SOLUTIONS
Name:
ID:
Sec.:
Q1.The data from 200 machined parts are summarized as follows:
edge condition
coarse
moderate
smooth
Serial: _____
depth of bore
above target
15
25
50
below target
10
20
80
a. What is the probability that a part selected has a moderate edge condition or a below-target bore
depth? (2-Points)
Let M: part selected has a moderate edge condition
B: part selected has a below-target bore depth
P (M or B )  P (M  B )  P (M )  P (B )  P (M  B )
 45 / 200  110 / 200  20 / 200
 135 / 200  0.675
b. If a part selected has a coarse edge condition, what is the probability that it does not have a belowtarget bore depth? (2-Points)
P (C  B ') P (C )  P (C  B )
P (B ' | C ) 

P (C )
P (C )
25 / 200  10 / 200

25 / 200
 15 / 25  0.60
c. Let E1: the event that a part selected has a smooth edge condition, E2: the event that a part selected has
above-target bore depth, are the two events independent? Explain. (3-Points)
No, because
P (E 1 )  130 / 200  0.65, P (E 2 )  90 / 200  0.45, P ( E 1  E 2 )  50 / 200  0.25
P (E 1 )* P (E 2 )  0.65*0.45  0.2925  0.25  P ( E 1  E 2 )
So, they are not independent. Note: It can also be proved using the conditional probability
Q2. An inspector working for a manufacturing company has a 99% chance of correctly identifying
defective items and a 0.5% chance of incorrectly classifying a good item as defective. The company has
evidence that its line produces 0.9% of nonconforming items. What is the probability that an item selected
for inspection is classified as defective? (3-Points)
P (LD )  0.9%  0.009
Let LD: The selected item is truly defective
P (LD ')  1  0.009  0.991
LD’: The selected item is truly not defective
Let CD: The item is classified as defective
P (CD )  P (LD CD )  P (LD 'CD )  P (LD )P (CD | LD )  P (LD ')P (CD | LD ')
 0.009*0.99
0.0139
 0.005*0.991
King Fahd University of Petroleum & Minerals
Department of Mathematics & Statistics
STAT-319-Term081-Quiz2B-SOLUTIONS
Name:
ID:
Sec.:
Q1.The data from 200 machined parts are summarized as follows:
edge condition
coarse
moderate
smooth
Serial: _____
depth of bore
above target
15
25
50
below target
10
20
80
a. What is the probability that a part selected has a smooth edge condition or a below-target bore depth?
(2-Points)
Let Sm: part selected has a smooth edge condition
B: part selected has a below-target bore depth
P (Sm or B )  P (Sm  B )  P (Sm )  P (B )  P (Sm  B )
 130 / 200  110 / 200  80 / 200
 160 / 200  0.80
b. If a part selected has a moderate edge condition, what is the probability that it does not have a belowtarget bore depth? (2-Points)
P (M  B ') P (M )  P (M  B )
P (B ' | M ) 

P (M )
P (M )
45 / 200  20 / 200

45 / 200
 25 / 45  5 / 9  0.5556
c. Let E1: the event that a part selected has a smooth edge condition, E2: the event that a part selected has
above-target bore depth, are the two events independent? Explain. (3-Points)
No, because
P (E 1 )  130 / 200  0.65, P (E 2 )  90 / 200  0.45, P ( E 1  E 2 )  50 / 200  0.25
P (E 1 )* P (E 2 )  0.65*0.45  0.2925  0.25  P ( E 1  E 2 )
So, they are not independent. Note: It can also be proved using the conditional probability
Q2. An inspector working for a manufacturing company has a 99% chance of correctly identifying
defective items and a 0.5% chance of incorrectly classifying a good item as defective. The company has
evidence that its line produces 0.9% of nonconforming items. What is the probability that an item selected
for inspection is classified as defective? (3-Points)
P (LD )  0.9%  0.009
Let LD: The selected item is truly defective
P (LD ')  1  0.009  0.991
LD’: The selected item is truly not defective
Let CD: The item is classified as defective
P (CD )  P (LD CD )  P (LD 'CD )  P (LD )P (CD | LD )  P (LD ')P (CD | LD ')
 0.009*0.99
0.0139
 0.005*0.991