Probability Question

Question

A hospital is testing for patients for a certain virus. If a patient has the virus, the test is designed to return "positive" result. If a patient does not have the disease, the test should return a"negative" result. The test is not perfect, however, and may give an incorrect result.

•10% of the patient have the virus

•98% of patients who have the virus will test positive

•5% of the patients who don't have the virus will incorrectly test positive

Determine the possibility that a randomly selected patient's does not have the virus but tests positive

P(V'∩ positive)=

Choices:

-0.045

-0.05

-0.855

-0.018

Answer 1

The answer should be .045.

Assume 100 patients total

If 90 patients do not have the virus (given) and are tested, then

5% of those tested who are not infected will test positive (given)

So, 5% of 90 = 4.5, then 4.5/100 = .045