The purpose of this problem is to illustrate the dangers of statistics, especially with respect to categorical data and the use of conditional probabilities. In this example, the data may be used to support contradicting claims, depending on the inclinations of the person doing the reporting! The population in which we are interested is made up of males and females, those who are sick and not sick, and those who received treatment prior to becoming sick and who did not receive prior treatment. (In the questions below, assume that the treatment has no adverse side effects.) The population numbers are as follows.
(a) What is the conditional probability of being sick given that the treatment was received and the patient is a male?
(b) Considering only the population of males, should the treatment be recommended?
(c) Considering only the population of females, should the treatment be recommended?
(d) Considering the entire population, should the treatment be recommended?