Positive test Negative test es HIV Cell A Cell B not carry HIV Cell D Cell E Cell G Cell H
Positive test Negative test es HIV Cell A Cell B not carry HIV Cell D Cell E Cell G Cell H
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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February 19, 2021 at 4:35 PM
Imagine a hypothetical population of 1,000,000 people for whom these percentages hold exactly.
Positive test
Negative test
Total
Carries HIV
Cell A
Cell B
Cell C
Does not carry HIV
Cell D
Cell E
Cell F
Total
Cell G
Cell H
1,000,000
Positive test
Negative test
Total
Carries HIV
Does not carry HIV
Total
1,000,000
a) Assuming that 0.5% of the population of 1,000,000 people carries HIV, how many such carriers
are there in the population? How many non-carriers are there? Record these values in the table in
Cells C and F, respectively.
b) Consider for now just the carriers. If 97.7% of them test positive, how many test positive? How
many carriers does that leave who test negative? Record these values in the table in Cells A and B,
respectively.
c) Now consider only the non-carriers. If 92.6% of them test negative, how many test negative?
How many non-carriers does that leave who test positive? Record these values in the table in Cells
E and D, respectively.
d) Determine the total number of positive test results and the total number of negative test results.
Record these values in the appropriate places within the table.
Expert Solution
Step 1
(a)
Given that the population is,
N= 1,000,000
The percentage of people carries HIV is, 0.5%
The total number of people Carries HIV from the population of 1,000,000 is,
=1000000*0.5%
=1000000*0.005
= 5000
The percentage of people does not carries HIV is ,
= 100-0.5%=99.5%
The total number of people does not Carries HIV from the population of 1,000,000 is,
=1000000*99.5%
=1000000*0.995
= 995000
The cells C and f are filled in the table below.
| Positive test | Negative test | Totals | |
| Carries HIV | cell A | cell B | 5000 |
| Does not Carries HIV | cell D | cellE | 995000 |
| Totals | cell G | cell H | 1000000 |
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