Find the indicated probability.

Question

Find the indicated probability.

Refer to the table which summarizes the results of testing for a certain disease.

 

If one of the results is randomly selected, what is the probability that it is a false negative (test indicates the person does not have the disease when in fact they do)? What does this probability suggest about the accuracy of the test?

Answer 1

Let A be the event of “Negative Test Result” and B be the event of “subject has the disease”. Now,

P(negative test result | subject has the disease) =

P(A | B) =

P(A and B) / P(B) =

(4 / 309) / (124 / 309) =

4 / 124 =

1 / 31 =

0.0323.