Question 1068989
a certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive".
P(infected) = 1/200
P(not infected) = 199/200
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P(A) = 1/200 ; P(A') = 199/200
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P(B|A') = 0.1
P(B|A) = 0.8 ; P(B'|A) = 0.2
P(B|A) = P(test positive | infected) = 0.80 
P(A'|B) = P(is not infected | test positive) = 0.10 
 

a) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A|B). Round your answer to the' nearest tenth of a percent and do not include a percent sign.
P(A|B) = P(B and A)/P(B) = P(B|A)*P(A)/P(B)
= P(B|A)P(A)/[P(B and A)+P(B and A')
= P(B|A)P(A)/[P(B|A)P(A)+P(B|A')P(A')]
= [0.8*(1/200)]/[0.8*(1/200) + 0.1*(199/200)]
= 0.004/[0.004+ 0.104]
= 0.037
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Cheers,
Stan H.
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