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?
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?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Using the attached spreadsheet please show full steps to get the solution.
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?

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) =
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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.
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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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