Consider the following hypothetical facts: “One per cent of people in the world are rational. We have a test for rationality. If someone is rational, they have a 60% chance of passing. If someone is irrational, they have a 40% chance of passing. Adam was just given the test, and he passed.”
(a) Assume that Adam was drawn randomly from the world population. What is the probability that he is truly rational? Don’t bother with the long division. Expressing your answer as a ratio is fine.
(b) Predict the responses of a population of naive subjects who are asked to estimate the probability of Adam’s rationality, given the information above. Justify your answer. Describe the kinds of errors that they are likely t o make.