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

    我討厭數學,但有個統計問題讓我非常著迷。

  • It's a question that seems really, really simple, but it's stumped me.

    這是個非常簡單的問題,但卻難倒了我。

  • And not just me, it has stumped thousands of people around the world including math professors and leading statisticians.

    而且不只有我而已,全球數以千計的人,包含數學教授與統計學專家們都被難倒了。

  • But before we dive in, I'm going to introduce you to Zachery Crockett.

    但在我們深入討論前,我想要介紹你認識 Zachery Crockett。

  • He first introduced me to the puzzle, and I called him up to talk about it.

    他是告訴我這謎題的人,於是我打給他來討論。

  • My name is Zachery Crockett, I'm a writer for Priceonomics.

    我是 Zachery Crockett,我是幫 Priceonomics 撰文的作家之一。

  • Zachery and his girlfriend were stumped by the problem too.

    Zachery 和他女友也被這謎題難倒了。

  • We just sat there debating the answer to this problem for two hours, and I don't think any of us really understood it.

    花了兩小時辯論這謎題的答案,但我覺得其實我們兩個都沒有真的理解它。

  • 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.

    這道難倒所有人的謎題叫做蒙提霍爾問題,以讓這謎題出名的節目主持人而命名的。

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

    題目是像這樣的,有三道門,其中一道的後方有一輛新車。

  • Behind the other two are goats.

    另外兩道門後則是山羊。

  • Say you pick door number one.

    假設你選了一號門。

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

    蒙提則會打開其中一道,後面是山羊,你沒選擇的門,假設是三號門。

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

    問題來了,你可以改變選擇到二號門。

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

    你會換嗎?還是你會堅持自己原本的選擇?

  • 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.

    對蒙提霍爾問題起興趣後,我做了些研究,發現故事後還有一些秘辛。

  • You've never met a man who feared you a little bit because he thought you were much brighter than he was?

    你有沒有遇過某個男人,因妳比他聰穎得多而對妳敬而遠之的?

  • That's Marilyn Vos Savant in 1988 being interviewed by Joe Franklyn.

    這是 1988 年時,Marilyn Vos Savant 被 Joe Franklyn 訪問的片段。

  • Well, yeah maybe I've met a man or two, maybe a couple a hundred like that.

    或許有一、兩個男人有這個情況,好啦,很多男人都這樣。

  • Marilyn is very intelligent.

    Marilyn 非常聰明。

  • In fact, back when the Guinness World Records actually kept track of this, she was the world's highest IQ.

    事實上,當金氏世界紀錄開始紀錄 IQ 時,她是世上 IQ 最高的人。

  • She now writes for Parade Magazine and has for the last 20 years.

    到現在為止,她已經幫 Parade 雜誌寫作寫了 20 年。

  • 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.

    這個專欄上頭寫著,世上 IQ 最高的人會在這裡回答你的數學問題。

  • This brings us to September 9th, 1990, when a reader submitted to Marilyn... the Monty Hall Problem.

    這帶我們回到 1990 年 9 月 9 號,一名讀者向 Marilyn 提出蒙提霍爾的謎題。

  • Is it to your advantage to switch your choice of doors?

    到底更換選擇,是好是壞?

  • Now, if you're like me the obvious answer is no.

    如果你跟我一樣,很明顯會選擇不換門。

  • There are two doors so the chance of getting a car and not a goat is 50/50.

    剩下兩道門,所以得到車子的機率是一半一半。

  • Bing. Bang. Boom.

    乒砰蹦!

  • But that's the wrong answer, and Marilyn knew that.

    但這是錯的,Marilyn 當時也知道。

  • She replied: “Yes; you should switch.”

    她當時回覆:「沒錯,你該換。」

  • And here's why.

    原因如下。

  • Here are three doors.

    有三道門。

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

    兩道門後面是山羊,一道後面是車子。

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

    在盲選的狀態下,比起車子,你更容易選到山羊。

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

    事實上,你有三分之二的機會選到山羊,那我們把這件事當成主要的情景。

  • You pick door one.

    你選了一號門。

  • So now, Monty Hall, who knows what's behind all the doors, is forced to reveal a goat regardless of the door you pick.

    現在,知道所有門後面有什麼的蒙提霍爾,一定得要打開一道後面有山羊的門。

  • Since, in the most probable scenario you've also picked a goat, the only door left is the one with the car.

    最可能的情況是,你一開始選了有山羊的門,所以剩下的那道門,就是有車子的那道。

  • So, now Monty Hall asks, "Would you rather keep the door you've picked, or would you switch?”

    所以當蒙提霍爾問「你要保留你的選擇,還是改變?」

  • Well, you should most definitely switch.

    這個嘛,你當然要換。

  • If you do you get the car two-thirds of the time.

    如果你換,你會有三分之二的機會拿到車子。

  • 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.

    結果,當 Marilyn 正確地回答蒙提霍爾問題時,她收到數千封來自世界各地的信,說她完全錯了。

  • I think part of her was a little bit surprised that she received 10,000 letters calling her an idiot.

    我想她當時應該有點驚訝,竟然會收到一堆信件說她是笨蛋。

  • There was, without a doubt, a little bit of sexism at play here.

    當然,當時有點性別歧視。

  • Not only was her answer right, it wasn't anything new.

    她不但答對了,而且這答案也不是什麼新穎的觀點。

  • The first time the Monty Hall problem was really conceived was in 1975.

    蒙提霍爾問題第一次是在 1975 年出現的。

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

    柏克萊大學的 Steve Selvin 在美國統計學會會刊中提出這個問題。

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

    他提出機率是三分之二,而沒人與他爭論。

  • You know, over the next 15 years multiple other academics reiterated the same problem, and no one ever told them that they were wrong.

    接下來的 15 年間,許多學者也反覆提出這個結果,從來沒人站出來說他們是錯的。

  • Then in 1990 Marilyn answered the same question correctly, and people went bananas.

    而 1990 年 Marilyn 答對這個問題時,人們卻抓狂了。

  • Marilyn ended up tallying up what percentage of the 10,000 responses claimed she was wrong.

    Marilyn 後來計算了這 10,000 個說她錯了的回覆者佔了多少百分比。

  • Only 8% of readers actually agreed with her, and after subsequent columns, she was able to raise that to 56%.

    只有 8% 的讀者同意她的觀點,而在之後的專欄,她讓同意度升高至 56%。

  • And among academics: It was 35% among academics initially supporting it.

    而在學者界中,一開始時有 35% 的人支持此論點。

  • Around 70% of academics ultimately decided to agree with her.

    最後,七成的學者都決定同意她。

  • The only way she managed to get people on her side was by asking them to do the experiment themselves.

    她唯一使人們改變想法的方式,就是叫大家自己實驗看看。

  • Elementary, middle school, and high school teachers from all over the country wrote in, astounded that their students were able to prove her right.

    全國的國小、中學甚至高中老師都投書,驚訝地說他們的學生證明了 Marilyn 是對的。

  • 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.

    現在只要簡單的 Google 一下,就能找到 100 萬種解釋這機車問題的方式。

  • There's something about this problem that really strikes a chord with, not only statisticians, but just everyday problem solvers and people.

    這問題有個神奇的魔力,不但讓統計學家們著迷,也讓所有人著迷。

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

我討厭數學,但有個統計問題讓我非常著迷。

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三門問題:一道難倒無數人的數學題 (The math problem that stumped thousands of mansplainers)

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    Mackenzie 發佈於 2020 年 01 月 21 日
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