Refer to Example 2.26. Assume that the proportion of people in the community who have the disease is 0.05.

a. Given that the test is positive, what is the probability that the person has the disease?

b. Given that the test is negative, what is the probability that the person does not have the disease?

Answer:

Step 1 of 3:

Given that, the proportion of people in the community who have the disease is 0.05.

Let D denote the event that a person has the disease.

Let +ve represent the event that the test is positive. The values are given by

= 1- 0.05

= 0.95

and

= 1- 0.99

= 0.01.

Step 2 of 3:

a). To find the probability that the person has a disease, if the test is positive.

=

= 0.8390.

Therefore, the probability that the person has a disease, if the test is positive is 0.8390.