Question

Problem 9.
When insurance companies establish policies for covering screening tests for diseases, one
important factor is the value of the test predicting the disease. For example, for a certain type of
disease, insurance companies may only cover the test costs if the test improves the prediction of
having the disease by 90%. To help decide coverage policy for a new test, use the following data
to help decide whether the test should be covered:

Test Positive Test Negative

Have Disease 55 12
Do Not Have Disease 22 74
a) (1 pt) Find P(A) = P(Having the disease among everyone)
b) (1 pt) Find P(B) = P(Testing positive for everyone)
c) (1 pt) Find P(A and B) = P(Having the disease and testing positive).
d) (1 pt) Find P(A | B) = P(Having the disease given tested positive).
e) (6 pts) Should the test be covered? What is your conclusion? Justify your answer using the
conditional probabilities above, i.e. compute the percent of increase from P(A) to P(A|B).

Answer 1