I have read through around 10 articles and webpages on this problem, and still don’t understand. I’ve run simulations and yes, switching does get you better odds, but why?
In: Mathematics
When you picked your door, you had a one in three chance of choosing the right door, so there was a two in three chance that the right door is one of the others.
Then Monty opens one door, and gives you the choice to swap.
Nothing has changed about the probabilities. You still have a one in three chance of having picked the right door, and there’s still a two in three chance that the right door is one of the other two. The only thing that changed is that now you know that, if you picked the wrong door to begin with, there’s only one option left, so, if you were wrong with your guess, that has to be the right door. So if you were wrong 2/3 of the time, that is likewise the right door 2/3 of the time.
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