Conditional probabilities are important not only in statistics but in many other areas of human reasoning and decision making. A problem, however, is that the human brain does not deal well with conditional probabilities. One reason is that we fail to take into account the effect that changes in base rates have on probability estimates. This can be illustrated with the Blue Cabs and Green Cabs problem. Problem is to determine probability that he was hit by a green cab given that he testifies he was hit by a green cab.
People invariably overestimate the probability that the victim was in fact hit by a green cab.
They do so because they do not give adequate weight to the differences in base rates. The formal mathematical procedure for computing conditional probabilities is to use Bayes Theorem. But this mathematical approach is a bit confusing and users are apt to make errors when plugging values into the appropriate equation. An alternative is to use a 2 x 2 matrix with scaled axes, as shown in class. The matrix has many applications.