Yearly automobile inspections are required for resi- dents of the state of Pennsylvania. Suppose that 12% of all inspected cars in Pennsylvania have problems that need to be corrected. Unfortunately, Pennsylvania state inspections fail to detect these problems 20% of the time. On the other hand, assume that an inspection never detects a problem when there is no problem. Consider a car that is inspected and is found to be free of problems. What is the probability that there is indeed something wrong that the inspection has failed to uncover?

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Yearly automobile inspections are required for resi- dents of the state of Pennsylvania. Suppose that 12% of all inspected cars in Pennsylvania have problems that need to be corrected. Unfortunately, Pennsylvania state inspections fail to detect these problems 20% of the time. On the other hand, assume that an inspection never detects a problem when there is no problem. Consider a car that is inspected and is found to be free of problems. What is the probability that there is indeed something wrong that the inspection has failed to uncover? 

A20
7
NN
1 Automobile inspections
2
3 Given Probabilities:
4
P(inspected car has problems)
5 P(inspected car has no problems)
6
P(no problem found | inspected car has problems)
P(problem found | inspected car has problems).
8
P(no problem found | inspected car has no problems)
9 P(problem found | inspected car has no problems)
10
24
NP
25
26
27
B
Ready
I UV
11 1. The goal is to find P(inspected car has problems | no problem was found).
12
13 P(inspected car has problems | no problem was found) =
14
P(inspected car has problems AND no problem found)/P(no problem found) =
15
16
17
18
19
20 2. Provide a brief clarification discussion about your results.
21
22
23
P9-05
H✓
fx 2. Provide a brief clarification discussion about your results.
A A
A
P(no problem found | inspected car has problems)*P(inspected car has problems)/
(P(no problem found | inspected car has problems)*P(inspected car has problems) +
P(no problem found | inspected car has no problems)*P(inspected car has no problems))
which is equal to ...(results)
P9-39
✓ A✓
V
121
Probability
+
C
%-
Number
D
Tell me
Conditi
Format a
Cell Style
E
Transcribed Image Text:A20 7 NN 1 Automobile inspections 2 3 Given Probabilities: 4 P(inspected car has problems) 5 P(inspected car has no problems) 6 P(no problem found | inspected car has problems) P(problem found | inspected car has problems). 8 P(no problem found | inspected car has no problems) 9 P(problem found | inspected car has no problems) 10 24 NP 25 26 27 B Ready I UV 11 1. The goal is to find P(inspected car has problems | no problem was found). 12 13 P(inspected car has problems | no problem was found) = 14 P(inspected car has problems AND no problem found)/P(no problem found) = 15 16 17 18 19 20 2. Provide a brief clarification discussion about your results. 21 22 23 P9-05 H✓ fx 2. Provide a brief clarification discussion about your results. A A A P(no problem found | inspected car has problems)*P(inspected car has problems)/ (P(no problem found | inspected car has problems)*P(inspected car has problems) + P(no problem found | inspected car has no problems)*P(inspected car has no problems)) which is equal to ...(results) P9-39 ✓ A✓ V 121 Probability + C %- Number D Tell me Conditi Format a Cell Style E
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