document.write( "Question 1191533: 9% of population has a symptom of a disease. If one tests a symptomatic person, probability of testing positive is p=0.78. If one tests a person without symptoms, the probability is p=0.06. If you test a random person what is the probability of the test returning positive results? What is the probability of a positive testing person actually having a disease? \n" ); document.write( "

Algebra.Com's Answer #823349 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "9% of population has a symptom of a disease.
\n" ); document.write( "If one tests a symptomatic person, probability of testing positive is p=0.78.
\n" ); document.write( "If one tests a person without symptoms, the probability is p=0.06.
\n" ); document.write( "(a) If you test a random person what is the probability of the test returning positive results?
\n" ); document.write( "(b) What is the probability of a positive testing person actually having a disease?
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document.write( "(a)  A random person EITHER has symptoms of the disease with the probability 0.09 \r\n" );
document.write( "                       OR   has no symptoms with the probability of 1 - 0.09 = 0.91.\r\n" );
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document.write( "     If the person has symptoms of the desease,    then he contributes 0.09*0.78 to the probability to get a positive test.\r\n" );
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document.write( "     If the person has no symptoms of the desease, then he contributes 0.91*0.06 to the probability to get a positive test.\r\n" );
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document.write( "     So, the total probability to get the positive test is \r\n" );
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document.write( "         P = 0.09*0.78 + 0.91*0.06 = 0.1248.    ANSWER\r\n" );
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document.write( "(b)  This probability is 0.78, as stated in the problem.    ANSWER\r\n" );
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