  The Monty Hall problem is notorious for its deceptive simplicity. Although
today it is widely used as a provocative thought experiment to introduce
Bayesian thinking to students of probability, in the not so distant past it was
rejected by established mathematicians. This essay provides some historical
background to the problem and explains why it is considered so
counter-intuitive to many. It is argued that the main barrier to understanding
the problem is the back-grounding of the concept of dependence in probability
theory as it is commonly taught. To demonstrate this, a Bayesian solution is
provided and augmented with a probabilistic graphical model (PGM) inspired by
the work of Pearl (1988, 1998). Although the Bayesian approach produces the
correct answer, without a representation of the dependency structure of events
implied by the problem, the salient fact that motivates the problem's solution
remains hidden.
