re: Marilyn vos Savant and the history of the Montel Hall question

I don’t follow her logic. We’re ultimately presented with information that a prize is behind one of two doors. Why should it matter which one is called door number 1, 2, or 3? Why should it matter that the original question was posed as if the odds were 1 in 3?

Let’s work it backwards. There are two doors. A prize is behind one. The odds of correctly guessing which door the prize is behind is 50/50, right? You choose one. I ask you if you want to change your mind. If you do and choose the other door, did the odds of correctly guessing suddenly change? Or is it still 50/50 odds? If so, explain. What about if I suddenly say, “Would you change your mind if I told you there was another door that did NOT have a prize behind it, would you change your mind?” Would that additional question and fact suddenly change the odds to 1 out of 3? What if I said there were 100 additional doors that a prize was NOT behind? Does that make the original question anything different than a 50/50 chance?

I still don’t understand how her answer is regarded as correct.