Conditional probability

1. The table below represents hypothetical data on 130 people taking an inkblot test for

bureaucratic pomposity disorder (BPD). Use the data to compute the 4 conditional

probabilities defined by the screening tests. Is the test a good one, in your judgment? Why or

why not? Be sure to assign letters to represent events and use mathematical notation in your

explanation.

a. What is the probability that someone has the disease given that the test shows apositive

reading? (positive predictive value PPV)

b. What is the probability that someone does not have the disease given that the test shows a

negative reading? (negative predictive value NPV)

c. What is the probability that someone tests positive given that he/she has the disease?

(sensitivity)

d. What is the probability that someone tests negative given that he/she does not have the

disease? (specificity)

e. In your judgment, is this a good test? Why or why not?

Test Results Positive Negative Total Present 60 40 100 BPD Absent 20 10 30 Total 80 50 130