A variant of the Monty Hall problem (the 7th one on this quiz) went semi-viral a couple months ago. For me at least, I may be able to walk through the reasoning of the original problem, and I may be able to convince myself it's correct, but it's very hard to build an intuition for why it's correct that feels truly sound. So I thought it'd be interesting to have a quiz to contort the original problem in as many ways as possible to challenge my understanding and intuition. Try it out! |
And the reasoning remains the same - when you pick a door you have 1/3 chance to pick the car, meaning the two other doors have a 2/3 chance to contain it. When he reveals a goat, my door is still 1/3 and the other one is still 2/3, so I should switch just like when he intentionally reveals the goat.
I should add the credit line, looks like I left it off for that one, though I think the general concept is pretty common.
One possible intuition is that when Monty opens a goat door in the original problem, the fact that he didn't open the other non-chosen door gives evidence that that door has a car (because it's more likely he doesn't open if it does have a car than if it has a goat).
In the "Monty Fall" variant, it's equally likely that he opens it whether it has a car or not. So the fact that it wasn't opened doesn't give you additional evidence for what's inside it.