VWICIICSS S statement? 10. To show how various factors influence probability, here are variations of Example 7 on HIV testing. a. Suppose that the population is 30,000 rather than 10,000, with the same test accuracy (98%)) and percent of HIV incidence the same (0.5%). What is the probability that a person who tests positive does have the HIV virus? b. Suppose there is a new test for the HIV virus that is 99% accurate (rather than the 98% in Example 7). Use a population of 20,000 but still with an HIV incidence of 0.5%. What is the probability that a person who tests positive does have the HIV virus? c. Suppose that the incidence of the HIV virus in one population is 3% (rather than the 0.5% of Example 7). Use a population of 10,000 and a test accuracy of 98%. What is the probability that a person who tests positive does have the HIV virus?

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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10.. A,b,c
CVCItJ 21 und D, 51VO3 the 1 (1|D)
P(A) Pelationship discussed in this section.
b. If A and B are independent, is P(A|B) = P(B|A)?
9. A cab was involved in a hit-and-run accident at night. Two cab companies, Blue Cab and
Green Cab, together own 1000 of the cabs in the city. Of these cabs, 85% are Green and
15% are Blue. A witness said that the cab in the accident was a Blue Cab. The witness was
tested in similar conditions and made a correct identification 80% of the time. What is the
probability that the cab in the accident was a Blue Cab, given the witness's statement?
10. To show how various factors influence probability, here are variations of Example 7
on HIV testing.
a. Suppose that the population is 30,000 rather than 10,000, with the same test
accuracy (98%.) and percent of HIV incidence the same (0.5%). What is the
probability that a person who tests positive does have the HIV virus?
b. Suppose there is a new test for the HIV virus that is 99% accurate (rather than the 98%
in Example 7). Use a population of 20,000 but still with an HIV incidence of 0.5%.
What is the probability that a person who tests positive does have the HIV virus?
c. Suppose that the incidence of the HIV virus in one population is 3% (rather than
the 0.5% of Example 7). Use a population of 10,000 and a test accuracy of 98%.
What is the probability that a person who tests positive does have the HIV virus?
11. In a polling of 400 parents, 20% had a high income. Fifty high-income parents oppose
school vouchers. Vouchers are supported by 160 low-income parents.
a. Complete the table, using the data above:
High-income
Low-income
Totals
Support vouchers
Transcribed Image Text:CVCItJ 21 und D, 51VO3 the 1 (1|D) P(A) Pelationship discussed in this section. b. If A and B are independent, is P(A|B) = P(B|A)? 9. A cab was involved in a hit-and-run accident at night. Two cab companies, Blue Cab and Green Cab, together own 1000 of the cabs in the city. Of these cabs, 85% are Green and 15% are Blue. A witness said that the cab in the accident was a Blue Cab. The witness was tested in similar conditions and made a correct identification 80% of the time. What is the probability that the cab in the accident was a Blue Cab, given the witness's statement? 10. To show how various factors influence probability, here are variations of Example 7 on HIV testing. a. Suppose that the population is 30,000 rather than 10,000, with the same test accuracy (98%.) and percent of HIV incidence the same (0.5%). What is the probability that a person who tests positive does have the HIV virus? b. Suppose there is a new test for the HIV virus that is 99% accurate (rather than the 98% in Example 7). Use a population of 20,000 but still with an HIV incidence of 0.5%. What is the probability that a person who tests positive does have the HIV virus? c. Suppose that the incidence of the HIV virus in one population is 3% (rather than the 0.5% of Example 7). Use a population of 10,000 and a test accuracy of 98%. What is the probability that a person who tests positive does have the HIV virus? 11. In a polling of 400 parents, 20% had a high income. Fifty high-income parents oppose school vouchers. Vouchers are supported by 160 low-income parents. a. Complete the table, using the data above: High-income Low-income Totals Support vouchers
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