The Simple Question that Stumped Everyone Except Marilyn vos Savant

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Marilyn vos Savant photo courtesy of: Ethan Hill

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[BubbleOnPlumb]

I would have switched to door #2 as well but for a very different reason. I would have assume that the goats would need to be kept as far apart as possible so they would be less likely to incite each other into making noise and thus giving their relative positions away. Putting the car in between them would help keep them out of each other's sight. I might just have won the car because I knew more about goats than mathematics in that instant!

[mlg]

I had the honor of having dinner with this lady while I was in college. Smart as hell, but very down-to-earth.

[johnnyw]

The way my brain understood it is this:
If you pick the door with a goat and you switch, you win!
If you pick the door with a car and you switch, you lose.

You have a 2 in 3 chance of picking a door with a goat. And a 1 in 3 chance of picking a door with a car.

Simple!

[LeChuck]

the example with the 100 doors finally explains it to understand it better

[tiffsaver]

I am most impressed with the math professor who publicly admitted his mistake. It is so refreshing to see someone who will actually take responsibility for their errors, regardless of how embarrassing it may be. If only our politicians could show as much humility. Much respect.

[fooojin]

People humbly and publicly admitting to be wrong, if only that existed today.

[samdavis]

I think there's a simpler way of explaining this puzzle. If you choose the correct door and switch you will be wrong. If you choose the incorrect door and switch you will be right ( because the other wrong door gets eliminated), and you choose the wrong door 2/3 times

[johnsdeath]

I look at it this way. There are only three possibilities:
1- you pick the car, so the host shows one of the 2 goats - then you should not switch door
2- you pick goat 1, so the host shows goat 2 - you must switch door
3 - you pick goat 2, so the host shows goat 1 - you must switch door
Therefore there is 2 out of 3 chance that switching your door choice will get you the car

[dustingre]

The best thing about this video is a reminder that when people publicly stated something incorrect, they used to express accountability and humility. That never happens anymore.

[nateblack]

This hurts my brain. But even high level mathematicians didn't understand it at first so I can't feel too bad for not getting it.

[knurdyob]

It gets even simpler when you ask yourself: with a 1/3 chance of getting the prize, after choosing your door, are you more likely to have picked right or wrong? Being that the answer is obviously that you are more likely to have picked the wrong door, and one of the other doors was confirmed to be wrong, you should switch doors. Either that, or you're admiting that you think you picked the right one on the first try.

[ShivSingh-ioeh]

When you initially explained that the other door would have a 2/3rd probability of a car being behind it, i couldn't understand it one bit. But i loved the explaination including a 100 doors where 98 were removed. That explaination immediately clicked to me and now I get it! What an interesting question. I always love these kinds of probability questions cuz they make me use my brain in ways I don't get to use while studying 😅

[BillyViBritannia]

Simpler explanation; assume you always switch:
If you initially picked a goat, you win. If you initially picked the prize you lose.
What's more likely?

[aetherllama]

First encountered this in high school. I tried to explain: "if you switch it's like picking 2 doors instead of 1", which convinced very few classmates. The teacher noted that I had good intuition and poor articulation. So true.

[fmjtgfy]

This is a no-brainer for me. I barely graduated high school but was easily accepted as tutor for statistics at SF Community College

[murrayspiffy]

I've long understood the Monty Hall solution - but extrapolating the information scale to 100 doors - makes complete sense - knowing that the "one door" is hot - and that you have a 98% chance of being wrong on your first door choice.

[eliasgermer]

A good way to think about this problem is: You first choose one door. You are then able to change your choice to BOTH the other doors. you get a car even if one of the doors have a goat behind it. This is the exact same thing as to show the goat beforehand.

[johnroush]

It makes total sense when mapped out. I guess the difficulty comes in understanding why "switching" doors increases your odds at all. I got hung up on the "switching" part having any impact, instead of realizing that it's making a new selection with better odds. We used to do simple stuff like this in grade school, it's kinda crazy how a little bit of language can subvert your logical faculties.

[NRClips]

I used to be amazed on the quality of these videos, but seeing how much they've improved in just a few year, blows my mind.

[daboffey]

To me, the answer is obvious - how can opening one unchosen goat door increase the probability of the first chosen door being the car door?