Suppose the probability of being infected with a certain virus is 0.001. a test used to detect the virus is positive 99% of the time if the person test has the virus, and positive 5% of the time if the person does not have the virus. use bayes theorem to find the probability that a person is infected with the virus, given that they test positive. clearly show your work and how you are using the theorem.

0.0194

Step-by-step explanation:

Let's define the following events

A: a person is infected with the virus

B: a person test positive

: a person is not infected with the virus

We know that P(A) = 0.001, and then = 0.999. A test used to detect the virus is positive 99% of the time if the person test has the virus is equivalent to P(B|A) = 0.99. And positive 5% of the time if the person does not have the virus means =0.05. We want to find the probability that a person is infected with the virus, given that they test positive, i.e., P(A|B). Bayes Theorem tell us that =0.0194

2.83941151 would be the answer you're looking for! : )