certain virus infects one in every 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 10% 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".   a. Find the probability that a person has the virus given that they have tested positive, i.e. find P(A | B). b. Find the probability that a person does not have the virus given that they test negative, i.e. find P(not A | not B).

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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A certain virus infects one in every 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 10% 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".

 

a. Find the probability that a person has the virus given that they have tested positive, i.e. find P(A | B).


b. Find the probability that a person does not have the virus given that they test negative, i.e. find P(not A | not B).

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