document.write( "Question 1194015: A certain virus infects one in 400 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 8% of the time if the person does not have the virus. Let A be the event the person is infected and B be the event the person tests positive.
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Algebra.Com's Answer #826099 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "A certain virus infects one in 400 people. A test used to detect the virus in a person is positive
\n" ); document.write( "90% of the time if the person has the virus and 8% of the time if the person does not have the virus.
\n" ); document.write( "Let A be the event the person is infected and B be the event the person tests positive.
\n" ); document.write( "Find the probability that a person has the virus given that they have tested positive (find P(A/B).
\n" ); document.write( "Round your answer to the nearest tenth of a percent and do not include a percent sign
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document.write( "Let the entire population will be 40000 persons.\r\n" );
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document.write( "Then 1/400 are infected, i.e.   = 100 persons.\r\n" );
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document.write( "Of these 100 persons, 90% are test positive, i.e. 90 persons.\r\n" );
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document.write( "These 90 are infected and test positive, at the same time; so, these 90 are the intersection of events A and B;\r\n" );
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document.write( "therefore, the numerator of the fraction in the formula for the conditional probability is 90.\r\n" );
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document.write( "    Next, among the rest  40000-100 = 39900 healthy persons,  8%,  or 0.08*39900 = 3192 are test positive.\r\n" );
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document.write( "    So, the total test positive is  90 + 3192 = 3282 persons.\r\n" );
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document.write( "Thus, event B has 3292 persons: this number is the denominator of the fraction for the conditional probability.\r\n" );
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document.write( "After these explanations, the conditional probability P(A|B) is\r\n" );
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document.write( "    P(A|B) =  =  = 0.027422 = 0.027 (rounded) = 2.7 %.    ANSWER\r\n" );
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