The Simple Question that Stumped Everyone Except Marilyn vos Savant

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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!

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

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.

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

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?

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

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.

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

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.

3:27 - "This is contingent on the host always opening a door with a goat." Yes, it is, which is why this restriction must be included within the problem as phrased, something the introduction to this video fails to do. That's actually a very common problem with this problem. It cannot be assumed that a goat had to be revealed simply because a goat was revealed unless the host's intention is incorporated into the problem. The host could have selected a door at random that simply happened to contain a goat. This legitimately changes the math to the Monty Fall/Blind Monty problem. This failure to accurately phrase the problem is frustratingly common.

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

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 😅

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.

So , I've known the Monty Hall problem since 2 decades, watched 100s of youtube videos on it too. But nobody cared to tell me that not many believed Marilyn vos Savant when she gave the correct answer. (Off course Steve Selvin gave the real proofs and solution with 3 prisoners problem). EDIT : I had no idea that so many dudes would be triggered by this comment. I'm a dude and I'm aware that a man's ego is just too fragile . But imagine being triggered by a harmless comment, almost all of the replies are by butthurt young boys and men. LOL

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?

Now I get it. He will never pick your door, and 2 out of 3 times you have the goat, so in those 2 out of 3 times you have the goat, he reveals the other goat and only the car is left. You win. The only time you lose is when you have the car to begin with.

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.

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.

3:33 You will be surprised how many people beleive that even in the 100-door game the player has a 50/50 odds between the remaing pair of doors.