just to chime in. The monty-hall problem is a pure math (probability-theory) and not statistics-excersize, since we know all the probabilities beforehand and do

just to chime in. The monty-hall problem is a pure math (probability-theory) and not statistics-excersize, since we know all the probabilities beforehand and don't estimate. It's very important to distinguish between bayesian inference and the bayesian theorem. The bayesian theorem can be proven and therefore must be true (if we accept the axioms). Bayesian inference has some real philosophical problems, since we often have no way to choose a justified prior. Frequentists approaches may also use the Bayesian theorem. I always like the blog-posts of the angry statistician and he also has one about the monty-hall problem: http://angrystatistician.blogspot.com/2012/06/bayes-solution-to-monty-hall.html http://angrystatistician.blogspot.com/2012/06/bayes-solution... The important difference is that one is the probability of P(x == car), which is 1/3, and one is P(x == car | y == goat). Just apply the bayes theorem and calculate it yourself!