ple. A test use the person has the virus and 8% of the time if False positive.) Let A be the event "the person i: = probability that a person has the virus given th r answer to the nearest tenth of a percent and c ne probability that a person does not have the viru Round your answer to the nearest tenth of a perce

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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 8% of the time if the person does not have the virus. (This 8% result
is called a false positive.) 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).
Round your answer to the nearest tenth of a percent and do not include a percent sign.
P(A|B)=
b) Find the probability that a person does not have the virus given that they test negative, 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') =
Question Help: D Video
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Transcribed Image Text: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 8% of the time if the person does not have the virus. (This 8% result is called a false positive.) 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). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(A|B)= b) Find the probability that a person does not have the virus given that they test negative, 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') = Question Help: D Video Submit Question P 40% here to search ** 12 Prtsc F11 F10 F8 F9 F7 F6 & @ %23 24 6 7 3 4 2 IT Y H. J G M C V Alt Alt B טא
Expert Solution
Step 1

Let A be the event that the person is infected and B be the event that the person tests positive.

A virus infects one in every 200 people.

That is, P(A)= 1/200= 0.005

Probability homework question answer, step 1, image 1

                              = 0.0478*100= 4.78≈ 4.8%( rounded to nearest tenth of a percent)

Thus, the probability that the person has a virus given that they tested positive is,

P(A|B)= 4.8  %

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