Exercise 20.4

Two statisticians go to the doctor and are both given the same prognosis: A 40% chance that the problem is the deadly disease $A$, and a 60% chance of the fatal disease $B$. Fortunately, there are anti-$A$ and anti-$B$ drugs that are inexpensive, 100% effective, and free of side-effects. The statisticians have the choice of taking one drug, both, or neither. What will the first statistician (an avid Bayesian) do? How about the second statistician, who always uses the maximum likelihood hypothesis?

The doctor does some research and discovers that disease $B$ actually comes in two versions, dextro-$B$ and levo-$B$, which are equally likely and equally treatable by the anti-$B$ drug. Now that there are three hypotheses, what will the two statisticians do?