A doctor has a testing kit, which she can use to test patients for the presence

Question

A doctor has a testing kit, which she can use to test patients for the presence of a certain virus. The test result is always either positive, or negative. If a patient who has the virus is tested, there is a 90% chance that the test will be positive. If a patient who does not have the virus is tested, there is a 90% chance that the test will be negative. It is known that 1% of people in Vancouver have the virus. A person is selected at random from the population of Vancouver, and given the test. It is positive. What is the probability that the person has the virus?

Explanation / Answer

P(Virus)=P(A)=0.01

P( Not A)=0.99

P( Positive/A)=0.90

P( Not positive/Not A)=0.90

P( A/Positive) = P(A)*P( Positive/A)/[P(A)*P( Positive/A)+P(not A)*P( Positive/not A)] = 0.01*0.90/[0.01*0.90+0.99*0.10]=0.0833333

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