Question

A screening test for a disease shows a positive result in 91% of all cases when the disease is actually present and in 7% of all cases when it is not. Assume that the prevalence of the disease is 1 in 650. If the test is administered to a randomly chosen individual, what is the probability that the result is positive

Answer 1

0.0713 = 7.13% probability that the result is positive.

Explanation:

Probability of a positive test:

91% of 1/650(has the disease).

7% of 1 - 1/650 = 649/650(does not have the disease). So

`p = 0.91(1)/(650) + 0.07(649)/(650) = (0.91 + 0.07*649)/(650) = 0.0713`

0.0713 = 7.13% probability that the result is positive.