Question

A diagnostic test has a probability 0.95 of giving a positive result when applied to a person suffering from a certain disease, and a probability 0.10 of giving a (false) positive when applied to a non-sufferer. It is estimated that 0.5 % of the population are sufferers. Suppose that the test is now administered to a person about whom we have no relevant information relating to the disease (apart from the fact that he/she comes from this population). Calculate the following probabilities:

a. that the test result will be positive
b. that, given a positive result, the person is a sufferer
c. that, given a negative result, the person is a non-sufferer
d. that the person will be misclassified

Answer 1

Answer:

a) 0.10425

b) 0.00475

c) 0.04975

d) 0

Step-by-step explanation:

a) Pr (the test result will be positive) = (0.95 × $\frac{0.5}{100}$ ) + ( 0.10 × $\frac{99.5}{100}$)

           = 0.00475 + 0.0995

           = 0.10425

b) Pr (positive result, the person is a sufferer) = 0.95 x $\frac{0.5}{100}$

           = 0.00475

c) Pr (negative result, non sufferer) = (1-0.95) x $\frac{99.5}{100}$

           = 0.04975

d) Pr ( person misclassified) = 0