The math problem that stumped thousands of mansplainers

The math problem that stumped thousands of mansplainers


I hate math, but there’s this statistics
problem that has me geeking out. It’s a question that seems really really simple but
it’s stumped me. And not just me, it has stumped thousands of people around the world
including math professors and leading statisticians.But before we dive in I’m going to introduce
you to Zachery Crockett. He first introduced me to the puzzle and I called him up to talk
about it. My name is Zachery Crockett, I’m a writer
for Priceonomics. Zachery and his girlfriend were confused by
the problem too. We just sat there debating the answer to this
problem for two hours and I don’t think any of us really understood it.
The puzzle we were all stumped by is called the Monty Hall Problem — named after the
host of the game show that made it famous. the problem goes like this: there’s a brand
new car behind one of three doors. Behind the other 2 are goats. Say you pick door 1.
Monty then shows you the goat behind one of the doors you DIDN’T choose – say, door
3. Now here’s the question: You’re allowed to change your answer to Door 2. Do you switch?
Or stick with your original choice? So yeah, I got interested in the Monty Hall
Problem, did a little research, and then I found out there was this whole second angle
to the story. You’ve never met a man that feared you a
little bit because he thought you were much brighter than he was?
That’s Marilyn Vos Savant in 1988 being interviewed by Joe Franklyn.
Yeah maybe I’ve met a man or two, maybe a couple a hundred like that.
Marilyn is very intelligent. In fact:Back when the Guinness World Records actually kept
track of this she was the world’s highest IQ.
She now writes for Parade Magazine and has for the last 20 years.
So the premise of the column was of course, like, here is the person with the world’s
highest IQ here to answer your challenging math questions.
This brings us to September 1990, when a reader submitted to Marilyn… the Monty Hall Problem.
Is it to your advantage to switch your choice of doors?
Now, if you’re like me the obvious answer is no. There’s no advantage of switching
doors at all, There are two doors so the chance of getting a car and not a goat is 50/50.
Bing. Bang. Boom. But that’s the wrong answer, and Marilyn
knew that. She replied: “Yes; you should switch.”
And here’s why. Here are 3 doors.
There’s a goat behind 2 and a car behind 1.
In a blind test, you’re more likely to pick a goat than a car. In fact, you’re 2/3RDS
likely so let’s use that as our main scenario. You pick door 1.
So now, Monty Hall, who knows what’s behind all the doors, is forced to reveal a goat
regardless of the door you pick. Since, in the most probable scenario you’ve also picked
a goat, the only door left is the one with the car.
So, now Monty Hall asks, “Would you rather keep the door you’ve picked, or switch?”
Well, you should most definitely switch. If you do you get the car 2/3rds of the time.
Turns out when Marilyn correctly answered the Monty Hall Problem, she received thousands
of letters from across the world telling her she was flat out wrong.
I think part of her was a little bit surprised that she received 10,000 letters calling her
an idiot. There was, without a doubt a little bit of sexism at play here. Not only was her
answer right, it wasn’t anything new. The first time the Monty Hall problem was
published was in 1975. This guy named Steve Selvin at Berkeley presented the problem in
The American Statistician. Selvin said you should switch and no one argued
with him. And over the next 15 years multiple other academics reiterated the same problem
without and no one ever told them that they were wrong.
Then in 1990 Marilyn answered the same question correctly and people went bananas.
Marilyn ended up and tallying up what percentage of the 10,000 responses claimed she was wrong.
Only 8% of readers actually agreed with her and after subsequent columns she was able
to raise that to 56%. And among academics: It was 35% among academics initially supporting
the answer. And about 70% of academics ultimately decided to agree with her.
The only way she managed to get people on her side was by asking them to do the experiment
themselves. Elementary, middle school, and high school teachers from all over the country
wrote in, astounded that their students were able to prove her right.It’s easy now to
do a simple google search of this little sucker of a problem and get a million explanations
on how to arrive at the right answer. There’s something about this problem that
really strikes a chord with, not only statisticians, but just everyday problem solvers and people.

100 Replies to “The math problem that stumped thousands of mansplainers

  1. Does the same principle apply when you’re asked if you’d like to switch your case in Deal or no deal?

  2. It doesn't matter if you switch because you are dealing with really small numbers the difference of the percentage would be really small. It would work sagnificanly if you had 100 doors and 98 were revealed.

  3. I don't know why this is soo complicated. You must switch because the host of the show WILL choose a door with a goat and hence the probability of there not being a goat inside the other door increases.

  4. The 40 second intro made me think it was one of the million dollar problems… In the end it's Monty hall?? That's very easy. I don't understand why it'll stump statisticians?

  5. This solution doesn’t work all the time only 2/3 of the time so I guess it is your best shot.
    If you did have the car as the door you picked that means so other 2 are goats, although they are only going to show one door, if you switch then you would lose the car to a goat.

  6. The MOnty Hall
    Problem is not the TV show, where a Box with the audience is there to pick as well. Therefore , the choice is 4 items.

  7. How did they kept the goats quite behind the doors ?? Because then anyone can choose the door which was quite and win the car as goat noise would come from other doors.

  8. Some people want not to switch because they want to have the feeling of knowing that their “win” if they did win, was one of the lowest chances of winning and thereby makes them a very lucky person. It can be a confidence boost for some people to win under lower chances of winning.

  9. On deal or no deal, when there’s only two cases left unopened (one on the stairs and one next to you) should you switch?

  10. DANG IT! I TABBED AHEAD SO I DIDN'T GET THE POINT THAT THE GOAT DOOR WAS REVEALED AFTER YOU PICKED A DOOR!

  11. Why do you use the term mansplaining? It's rude, sexist, and has no relationship to the actual subject!

  12. i tried showing this video to my boyfriend and he argued with me saying there was only two doors… epitome of mansplaining

  13. I created a randomized JavaScript tool to check if it's true and it is! Not swapping gives you chance of 1/3 , while swapping gives you 2/3.

  14. First of all, it seems like so many people were contesting her decision because she was known as the smartest person in the world and they wanted to prove smarter. Other than that, the logical answer to this problem seems to be that the original choice does not affect the overall outcome, as all it does is narrow it down to two choices. If you think of the first choice being just a distraction and jot affecting the outcome, it should be a 50/50 chance no matter your first choice. Im not a mathematician but this is my logical thinking on the subject.

  15. that isn't even mansplaining, it's just sexism??
    like isn't mansplaining a. man trying to uh… explain women's issues, like periods or something??
    math isn't a women's issue lol.

  16. Booo you should have started the question explaining there are 2 goats and 1 car… then it would be a super easy probability question.

  17. You successfully made a mathematical solution a lesson about the sexism even if it happened at another era. Nice… womansplaining!

  18. After I started reading the Wikipedia article on this, I gave up. Such a simple problem with an incredibly complex examination!

  19. For people commenting "mansplaining" is a made up word- yeah. That's the point of words. We make them up to denote, define or describe things. An apple is called so because we decided to call it an apple.

  20. The problem is that the video itself covers the topic in a simple, yet effective way, too bad they dragged their own message into this, should've kept it neutral in my opinion but im too busy watching Borders from one of the other Vox series

  21. With all due respect, the answer is no, because goats like to occupy doors in numerical order. Gimme my car behind 3.

  22. I had to black parts of the word and read man-s-plain-ers
    Man s Explain Ers
    Yup this is retardation

  23. U said that it stumped thousand mathematician and statisticians. Ok got it. If ur mathematician or statistician ur mansplainer

  24. I hope Vox recognizes, especially based on this comment section, why mansplaining is not only a myth, a complete non-phenomenon, but is also sexist.

  25. I just tried it on a post-it note at the beginning of the video. I started out with a 1/3 chance to pick the car. When one is revealed, that chance increases to 1/2. Normally, for example when you roll two dice, the chance of getting the same number is 1/6 * 1/6. However, because 1/3 of the doors are revealed, your chances are increasing, meaning it is instead (1/3) / (1/2), now making your chances 2/3, the same answer she got. Why is everyone in the comments so pissy? So what if they used pathos language in the title; everybody clickbaits now-a-days.

  26. Easier to visualize if you think of it as a million doors. You initially pick door 205,752. Monty then opens every other door except 743,305. Should you switch to 743,305?? Of course!!! The chances of picking it right at first were almost zero.

  27. Human has the word man inside despite having both sexes

    People:no big deal it’s just a word.

    Mansplaining strolls by

    People: heavy breathing

    Seriously the word means people who tried to explain smthg to someone who knew more than them. It originated from the cases of men in the past patronize professional women by acting like they know better. This video is almost just that. One of the world’s smartest women at that time explained the answer correctly, and a lot of angry letters from nobodies telling her they know better

  28. Many people don't get it (I got it immediately without needing the explanation), so let me explain as simple as possible. Forget everything you thought, just follow me here.

    You pick a door. There's a 2/3 chance you picked a goat and 1/3 you picked the car.

    You pick a door. A goat in another door is revealed.

    You got two doors left. There's not a 50/50 chance that you'll pick a door with the car. You've already picked a door, and there was 33.33% chance that door had the car. This still applies.

    Because of this, it is given that the chance of the other door having the car is 66.66%. One of the doors is guaranteed to have a car, since the third door, which you didn't pick, had a goat.

  29. I read comments while watching
    Seeing lots of "mansplaining"
    Here I am, video replaying
    Maybe I missed something

    Then oof.

    I just came here after reading "math problem"

  30. Wait what? What if i originally get the right answer and opened another door and see a goat? Should i still switch? God this video is useless

    Edit: i just watched vsauce's version and it's so much better and informative.

  31. It makes a lot of sense… come on, 2/3 possibilities of being wrong is a lot! 66.66% is a lot compared to 50%. And it’s seems worse when you see that 33.333 is your chance to be correct, I rather have 50% chance to be correct than 33.33… or I rather have 50% chance to be wrong than 66.666 chance to be wrong

  32. Mansplaining doesn't exist, everyone has the potential to do it and I have seen it in both genders. It is actually called over explaining.

  33. there's a loophole in the problem. yes you can choose the car in 2/3 and 1/3 pattern but it depends on where you place the goat and the car in three doors. so basically she's right and also wrong at the same time.

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