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'''The Problem:''' | '''The Problem:''' | ||
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There is a new test that will test for the HIV virus, but we are not sure of whether this test's results are usually correct or not. We are given the following information: | There is a new test that will test for the HIV virus, but we are not sure of whether this test's results are usually correct or not. We are given the following information: | ||
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Are the results usually correct, and what can you tell from the results? | Are the results usually correct, and what can you tell from the results? | ||
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'''The Solution:''' | '''The Solution:''' | ||
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| + | First, we determine the probability that a random person within the population tests positive. Remember, this person will be selected at random, so we have no clue whether or not he/she actually has the virus or not. | ||
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| + | <math>P(+) = P (+ \cap HIV) + P(+ \cap no HIV)\!<\math> | ||
Revision as of 06:07, 5 October 2008
The Problem:
There is a new test that will test for the HIV virus, but we are not sure of whether this test's results are usually correct or not. We are given the following information:
$ P (+ | HIV) = 0.9, P (- | HIV) = 0.1\! $
$ P (+ | no HIV) = 0.1, P (- | no HIV) = 0.9\! $
We are also given that only $ 0.5%\! $ of the population has the HIV virus. The rest do not.
Are the results usually correct, and what can you tell from the results?
The Solution:
First, we determine the probability that a random person within the population tests positive. Remember, this person will be selected at random, so we have no clue whether or not he/she actually has the virus or not.
$ P(+) = P (+ \cap HIV) + P(+ \cap no HIV)\!<\math> $
