A Probability Model for Forced Binary Choices

In this article a natural extension of the beta-binomial distribution is developed.Forced binary choice situations are modeled such that each individual has a probability p of knowing the correct answer.(This probability is distributed f(p) across the population.)Hence each individual will guess at the correct answer with probability 1 . p.The observable random variable R, the total number of correct answers (both by knowing and guessing) out of k trials has a rather complicated distribution.However, when f(p) is distributed beta with parameters m and n, the distribution P(r; k, m, n) can be expressed in terms of the well-known Gaussian hypergeometric function.This distribution has implications for true-false tests, taste tests, and virtually every other forced binary choice situation.