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document.write( "A certain virus infects one in every 500 people.
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document.write( "A test used to detect the virus in a person is positive 90% of the time if the person has the virus
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document.write( "and 10% of the time if the person does not have the virus.
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document.write( "Let A be the event \"the person is infected\" and B be the event \"the person tests positive.\"\r
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document.write( " (a) Find the probability that a person has the virus given that he or she is tested positive.\r
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document.write( " (b) Find the probability that a person does not have the virus given that he or she is tested negative.\r
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document.write( "Solution\r
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document.write( "(a) To make the solution easier, let assume that we have a population of 100,000 persons in the city.\r\n" );
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document.write( " According to the input data, 
of them, i.e. 
= 200 are infected.\r\n" );
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document.write( " Of this 200 people, 90%, i.e. 0.9*200 = 180 are test positive.\r\n" );
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document.write( " The problem asks in (a), what is the ratio of the number of those who are test positives AND have the virus \r\n" );
document.write( " to the number of infected.\r\n" );
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document.write( " It is obvious that this ratio is P = 
= 0.9 = 90%. ANSWER\r\n" );
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document.write( " In the compact form, a formula for the probability (a) is P = 
= 0.9.\r\n" );
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document.write( "(b) The probability under question (b) is the ratio of the number of those who do not have a virus AND are tested negative\r\n" );
document.write( " to the number of those who do not have the virus.\r\n" );
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document.write( " The number of those who do not have the virus is 100000 - 0.002*100000 = 100000 - 200 = 99800.\r\n" );
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document.write( " Of them, the number of those who are tested negative is (1-0.1)*99800 = 0.9*99800 = 89820.\r\n" );
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document.write( " With these numbers, the probability (b) is\r\n" );
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document.write( " P = 
= 0.9. ANSWER\r\n" );
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document.write( " In the compact form, a formula for probability (b) is P = 
= 0.9.\r\n" );
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document.write( "Solved.\r
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
