The role of probability in solving the Monty Hall problem

[Fidel_Castronaut]

I see your  problem. You are assuming Monty cheats. Otherwise we know the probability.  Each door has a one third chance of revealing the prize and a two thirds chance of revealing a goat. By revealing a goat door we didn't choose, Monty gives a mathematical reason to switch doors.


It is counter intuitive.  And I remember being really bothered by this problem.  But the math does work.

There is no more parsimonious way than explaining the MH 'problem' than this post. 

You need to look at it in terms of simple probability and the fact that the presenter opens up a door you both (now) know contains a goat.