  Now consider another case. Suppose Janice and Danny are the same age and take all the same math and science classes through high school. They are both moderately good at math. In fact, they almost always get the same grades in math. On many occasions they come up with different answers for homework problems. As far as they have been able to determine, in those cases 40% of the time Janice has been right, 40% of the time Danny has been right, and 20% of the time they have both been wrong. Suppose they both know this interesting fact about their track records! Now they are in college together. Danny believes, on the basis of their track records, that on the next math problem they happen to disagree about, the probability that Janice’s answer is right equals the probability that his answer is right—unless there is some reason to think one of them has some advantage in this particular case (e.g., Danny has had a lot more time to work on it, or some other significant discrepancy in Disagreement Factors). Suppose further that on the next typical math problem they work on Danny thinks that neither of them has any advantage over the other this time around. And then Danny finds out that Janice got an answer different from his.