Question

The Covid-19 virus infects 10% of the people in a certain community. A test used to detect the virus in a person is positive 85% of the time if the person has the virus and 5% of the time if the person does not have the virus. (This 5% result is called a false positive). Let A be the event "the person has the virus" and B be the event "the person tests positive".

a) Find the probability that the test result is positive.

b) Find the probability that a person does not have the Covid-19 virus given that they test is positive.

Answer 1

We are given that Covid-19 virus infects 10% of the people in certain community and 'A' is the event that the person has the virus. Thus, we get:

P(A) = 10% = 0.1

=> P(A^c) = 1 - P(A) = 1 - 0.1 = 0.9

Moreover, we are given that 'B' is the event that the person tests positive. Now, we are given the test used to detect the virus in a person is positive 85% of the time if the person has the virus, thus we get:

P(positive test result | person has the virus) = P(B|A) = 85% = 0.85

Moreover, we are given that the test is positive 5% of the time if the person does not have the virus, thus we get:

P(positive test result | person doesn't have the virus) = P(B|A^c) = 5% = 0.05

a)

The probability that the test result is positive is given by:

b)

The probability that a person does not have the Covid-19 virus given that the test is positive is given by:

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