Exercise 15 2 percent of the population of a country are infected with a virus. The tests for antibodies against the virus are often, but not always, correct. In infected people, 95% of the tests show a positive result. In healthy people, 3% of the tests are positive. (i) Compute the probability that a person with a positive test is not infected (false positive test). (ii) Compute the probability that a person with a negative test is really not infected (true negative test).

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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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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Exercise 14 An urn contains 2 green, 2 blue, 2 red balls. We draw 4 balls without replacement.
(i) Describe a suitable sample space and the probability mass function.
(ii) Find the probability that among the first 3 chosen balls is 1 red ball, and the forth ball is red. Apply the multi-
plication formula.
Exercise 15 2 percent of the population of a country are infected with a virus. The tests for antibodies against the
virus are often, but not always, correct. In infected people, 95% of the tests show a positive result. In healthy people,
3% of the tests are positive.
(i) Compute the probability that a person with a positive test is not infected (false positive test).
(ii) Compute the probability that a person with a negative test is really not infected (true negative test).
Transcribed Image Text:Exercise 14 An urn contains 2 green, 2 blue, 2 red balls. We draw 4 balls without replacement. (i) Describe a suitable sample space and the probability mass function. (ii) Find the probability that among the first 3 chosen balls is 1 red ball, and the forth ball is red. Apply the multi- plication formula. Exercise 15 2 percent of the population of a country are infected with a virus. The tests for antibodies against the virus are often, but not always, correct. In infected people, 95% of the tests show a positive result. In healthy people, 3% of the tests are positive. (i) Compute the probability that a person with a positive test is not infected (false positive test). (ii) Compute the probability that a person with a negative test is really not infected (true negative test).
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