The following problem was given to 60 students and doctors at the famous Havarti Medical School (HMS): Assume there exists a test to detect a disease, say D, whose prevalence is 0.001, that is, the probability, P[D], that a person picked at random is suffering from D, is 0.001. The test has a false-positive rate of 0.005 and a correct detection rate of 1. The correct detection rate is the probability that if you have D, the test will say that you have D. Given that you test positive for D, what is the probability that you actually have it? Many of the HMS experts answered 0.95 and the average answer was 0.56. Show that your knowledge of probability is greater than that of the HMS experts by getting the right answer of 0.17.

A fair die is tossed twice (a die is said to be fair if all outcomes 1..., 6 are equally likely). Given that a 3 appears on the first toss, what is the probability of obtaining the sum 7 after the second toss?