There are two programs in a high school. Boys are a majority (65%) in program A, and a minority (45%) in program B. There is an equal number of classes in each of the two programs.
You enter a class at random, and observe that 55% of the students are boys. What is your best guess -- does the class belong to program A or to program B?
Not having memorized the formula for variance in binomial distributions, but intuiting that said principle was true, was my weaker reason for concluding B.
More saliently, the problem statement contains the gratuitous information that boys are a majority in program A. It's Kahneman and Tversky, for FSM's sake; therefore this information is used to mislead. Therefore, B.
0Richard_Kennaway
No principle, just the fact that the variance of the binomial distribution is p(1-p), which peaks at p=0.5.
Found in an old Kahneman & Tversky paper: