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  • 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 stumped 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.

  • You see the problem goes like this: there's a brand new car behind one of three doors.

  • Behind the other two are goats.

  • Say you pick door number one.

  • Monty then shows you the goat behind one of the doors you didn't choose - say, door three.

  • Now here's the question: you're allowed to change your answer to Door two.

  • Do you switch? Or do you stick with your original choice?

  • But 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 who 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.

  • Well, 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 9th, 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 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 three doors.

  • There's a goat behind two and a car behind one.

  • In a blind test, you're more likely to pick a goat than a car.

  • In fact, you're two-thirds likely, so let's use that as our main scenario.

  • You pick door one.

  • 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 would you switch?”

  • Well, you should most definitely switch.

  • If you do you get the car two-thirds 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 really conceived was in 1975.

  • So, this guy named Steve Selvin at Berkeley presented this problem in The American Statistician.

  • He contested that the odds were two out of three, and no one argued with him.

  • You know, over the next 15 years multiple other academics reiterated the same problem, 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 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 it.

  • Around 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.

I hate math, but there's this statistics problem that has me geeking out.

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The math problem that stumped thousands of mansplainers

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    Mackenzie posted on 2020/01/21
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