Math

ProbabilityQ&A LibraryA certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 85% 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".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 a percent rounded nearest fourth decimal place 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 as a percent rounded to the nearest fourth decimal place and do not include a percent sign.P(A'|B') = %Question

Asked Sep 18, 2019

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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 85% 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".

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 a percent rounded nearest fourth decimal place 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 as a percent rounded to the nearest fourth decimal place and do not include a percent sign.

P(A'|B') = %

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Step 1

It is given that one in every 200 people were infected by the virus.

Let the event A represent “the person is infected” and the event B represent “the person tests positive”.

That is, the probability of the person is infected is, P(A) = 1/200

The probability of the person is not infected is, P(A') = 199/200

*For having virus:*

P(True Positive) = 85%

P(True negative) = 15%

*For not having virus:*

P(False Positive) = 10%

P(False Negative) = 90%.

Step 2

**a) Probability that a person has the virus given that they test positive:**

The probability that a person has the virus given that they test positiv...

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