Probability in Virus TestingDate: 06/04/99 at 17:52:08 From: Bernie Warner Subject: Stats (Bayes Theorem) In a country, 1 person in 10,000 (.01%) has the EB virus. A test that identifies the disease gives a positive indication 99% of the time when an individual has the disease. However, 2% of the time it gives a positive indication when a person doesn't have the disease. a) If a randomly selected individual is tested and the test turns out positive, what is the chance that this individual has the virus? b) Construct a 2 by 2 table. I am having trouble constructing the table. I am also not sure what I am supposed to do with the numbers to arrive at the answer for (a). Date: 06/04/99 at 18:38:06 From: Doctor Anthony Subject: Re: Stats (Bayes Theorem) Initial Prob. Initial Prob. Has the virus Does not have virus Prob = 0.0001 Prob = 0.9999 --------------------------------------------- 0.00001 x 0.99 0.9999 x 0.02 Test is positive = 0.0000099 = 0.019998 0.00001 x 0.01 0.9999 x 0.98 Test is negative = 0.0000001 = 0.979902 Since we are told that the test is positive, the sample space is confined to the top row. 0.0000099 Prob has virus = -------------------- = 0.0004948 0.0000099 + 0.019998 With such a low probability of a person actually having the disease given a positive result, the test itself is practically worthless. - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ |
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