document.write( "Question 1195936: Suppose that 4% of all the patients are infected with the virus (event V),
\n" ); document.write( "P(V) = 0.04.There exists a test for this viral infection. It is 95% reliable for infected patients and
\n" ); document.write( "99% reliable for healthy ones. That is, if a patient has the virus, the test shows that (event S) with
\n" ); document.write( "probability P(S | V) = 0.95, and if the patient does not have the virus, the test shows that with
\n" ); document.write( "probability P(S^c|V^c) = 0.99. If a person is tested positive, what is the probability that he/she is infected? \n" ); document.write( "

Algebra.Com's Answer #828569 by ikleyn(52799) $\"\"$ $\"About$

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\n" ); document.write( "Suppose that 4% of all the patients are infected with the virus (event V), P(V) = 0.04.
\n" ); document.write( "There exists a test for this viral infection.
\n" ); document.write( "It is 95% reliable for infected patients and 99% reliable for healthy ones.
\n" ); document.write( "That is, if a patient has the virus, the test shows that (event S) with
\n" ); document.write( "probability P(S | V) = 0.95, and if the patient does not have the virus, the test shows that with
\n" ); document.write( "probability P(S^c|V^c) = 0.99.
\n" ); document.write( "If a person is tested positive, what is the probability that he/she is infected?
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document.write( "First, let's calculate the probability that a person is tested positive.\r\n" );
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document.write( "It is  P(tested positive) = P(V)*0.95 + P(V^c)*(1-0.99) = 0.04*0.95 + (1-0.04)*(1-0.99) = 0.0476.\r\n" );
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document.write( "Next, the probability that the person is infected is  P(V) = 0.04  (given).\r\n" );
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document.write( "They want you find the conditional probability\r\n" );
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document.write( "    P(a person is infected | he/she is tested positive)  =  = \r\n" );
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document.write( "                                                         =  = 0.7983  (rounded).    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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