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 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') =

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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 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') =
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Transcribed Image Text:M0/1 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 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 9% e here to search *** F12 Prisc ** FIL F10 F9 F7 & %23 6 7 3 4. Y U IT E 11 J G S C Ctri Alt Alt
Expert Solution
Step 1

Let's draw tree diagram from given information ,  

A : Event that the person is infected 

P( A ) = 1/400 = 0.0025

B : Event that the person tests is positive.  

Probability homework question answer, step 1, image 1

we have , 

P( A ) = 0.0025 ,  P( A') = 0.9975

P( B | A ) = 0.9 ,  P( B' | A ) = 0.1

P( B | A' ) = 0.08 ,  P( B' | A' ) =  0.92

 

 

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