難倒眾人，卻唯獨沒難倒瑪麗蓮·沃斯·莎凡特的簡單問題：英語精讀講義

It's quite fitting that Marilyn vos Savant's last name in French means learned. 表達脈絡

瑪麗蓮·沃斯·莎凡（Marilyn vos Savant）的姓氏在法語中的意思是「博學」，這再適合不過了。

Learning came easy to her considering she has an IQ of 228. 片語搭配

鑑於她的智商高達228，學習對她來說簡直輕而易舉。

Vos Savant was born in St. Louis, Missouri

沃斯·莎凡出生於密蘇里州的聖路易斯，

on August 11, 1946

時間是1946年8月11日，

to immigrants from Germany and Italy.

父母是來自德國和義大利的移民。

Her parents never told her she was exceptional.

她的父母從未告訴過她她有多特別。

She once said in an interview,

她曾在一次採訪中說，

"No one really paid much attention to me,

「真的沒有人太在意我，

mostly because I was a girl,

主要是因為我是個女孩，

and I accepted that."

而我也接受了這一點。」

But the world would pay attention in 1985 表達脈絡

但在1985年，全世界都將目光投向了她，

when she topped the Guinness Book of World Records list 文化背景

當時她榮登《金氏世界紀錄大全》榜首，

as the smartest person in the world.

被稱為世界上最聰明的人。

She was nearly 40 when she shot into the spotlight. 慣用語

她一舉成名時已經將近40歲了。

Parade Magazine wrote a profile on her

《Parade》雜誌為她寫了一篇人物專訪，

and readers had so many questions for her 文法

讀者們向她提出了各式各樣的問題，

that the magazine offered her a Sunday column,

以至於該雜誌為她開設了一個週日專欄——

"Ask Marilyn," which exists to this day. 片語搭配

《問問瑪麗蓮》，這個專欄至今依然存在。

In this column,

在這個專欄中，

she ignited one of the fiercest debates 慣用語

她引發了21世紀

in probability of the 21st century.

機率學界最激烈的爭論之一。

In 1990,

在1990年，

a reader asked her the following question:

一位讀者向她提出了這樣一個問題：

"Suppose you're on a game show and you're given the choice of three doors. 文法

「假設你正在參加一個電視遊戲節目，你有三扇門可以選擇。

Behind one door is a car.

一扇門後面是一輛汽車。

Behind the others, goats.

另外兩扇門後面是山羊。

You pick a door, say number one, 表達脈絡

你選擇了一扇門，比如說一號門，

and the host who knows what's behind the doors

而知道門後有什麼的主持人，

opens another door, say number three,

打開了另一扇門，比如說三號門，

which has a goat.

後面是一隻山羊。

He says to you,

他對你說，

"Do you want to pick door number two?

『你想改選二號門嗎？』

Is it to your advantage to switch your choice of doors?" 片語搭配

改變選擇對你有利嗎？」

This is known as the Monty Hall problem, 文化背景

這就是著名的「蒙提霍爾問題」，

named after the former host of the game show

以遊戲節目

"Let's Make a Deal."

《達成交易》（Let's Make a Deal）的前主持人命名。

Is it behind door number one

它是在一號門後面，

or door number two

還是二號門後面，

or door number three?

抑或是三號門後面？

So, would it be in your interest

那麼，從一號門

to switch from door number one to door number two?

換到二號門符合你的利益嗎？

I'll give you a few seconds to think about it.

我給你幾秒鐘時間思考一下。

Most people assume that both doors are equally likely to have the prize, 片語搭配

大多數人認為兩扇門後有獎品的機率是一樣的，

so they don't see the benefit of switching.

所以他們覺得換門沒好處。

However, Vos Savant replied,

然而，沃斯·莎凡回答說：

"Yes, you should switch.

「是的，你應該換。

The first door has a one in three chance of winning, 片語搭配

第一扇門中獎的機率是三分之一，

but the second door has a two in three chance."

但第二扇門中獎的機率是三分之二。」

She got so much heat for this response 慣用語

她因為這個回答遭到了猛烈的抨擊，

and couldn't have imagined the backlash that would follow. 文法

並且根本無法想像隨之而來的強烈抵制。

She received thousands of angry letters and said 90% of them told her she was wrong.

她收到了成千上萬封憤怒的信件，她說其中90%都在指責她錯了。

Scott Smith, who has a PhD from the University of Florida, wrote,

擁有佛羅里達大學博士學位的史考特·史密斯寫道：

"There is enough mathematical illiteracy in this country

「這個國家已經有足夠多數學文盲了，

and we don't need the world's highest IQ propagating more.

我們不需要世界上智商最高的人來進一步推波助瀾。

Shame."

真丟人。」

Here's a letter from Professor Robert Sachs of George Mason University:

這是一封來自喬治梅森大學羅伯特·薩克斯教授的信：

"You blew it. 慣用語

「你搞砸了。

As a professional mathematician,

作為一名職業數學家，

I'm very concerned with the general public's lack of mathematical skills.

我非常擔憂公眾在數學技能上的缺乏。

Please help by confessing your error

請承認你的錯誤以提供幫助，

and in the future being more careful."

並在未來更加謹慎。」

Don Edwards of Oregon put it this way:

奧勒岡州的唐·愛德華茲這樣表述：

"Maybe women look at math problems differently than men."

「也許女性看待數學問題的方式與男性不同。」

But actually the people who sent her the not so friendly letters were absolutely wrong. 語氣意圖

但實際上，那些給她寄來不太友善信件的人完全錯了。

Switching your door does increase your probability of winning the prize. 文法

換門確實會增加你贏得獎品的機率。

When you first choose door number one,

當你最初選擇一號門時，

there's a one in three chance that the prize is behind that one

獎品在那扇門後的機率是三分之一，

and a two in three chance that it's behind one of the other two.

而在另外兩扇門後的機率是三分之二。

But then the host steps in and gives you some help 片語動詞

但隨後主持人介入並給了你一些幫助，

by opening up the door they know is a loser.

打開了他們知道沒有獎品的那扇門。

So door number two must have the rest of the chances. 文法

所以二號門必定包攬了剩下的機率。

It went from having a one in three chance 文法

它贏得獎品的機率從三分之一

to a two in three shot at the prize.

變成三分之二。

Since the host filtered out the bad door for you, door number three, 片語動詞

既然主持人為你剔除了那個錯誤的門，也就是三號門，

switching doubles your odds of winning. 片語搭配

換門就能讓你的勝算翻倍。

Or put another way, 表達脈絡

或者換句話說，

So yeah, to door number two and

所以沒錯，轉向二號門，並且

thank you for the extra 33.3%.

感謝那多出來的33.3%。

The outcry against Vos Savant was so extreme

針對沃斯·莎凡的抗議聲如此極端，

that she felt compelled to devote several other columns 講解

以至於她覺得自己不得不又專門寫了幾篇專欄文章

to explaining her logic.

來解釋她的邏輯。

She noted that the benefits of switching can be proven

她指出，如果你把窮盡所有可能性的

if you were to play through the six games 文法

六種遊戲情況都玩一遍，

that exhaust all possibilities. 片語搭配

就能證明換門的好處。

This is contingent on the host always opening a door with a goat. 用詞

其前提條件是，主持人總是會打開一扇有山羊的門。

Mapping out all the possibilities shows there's a higher chance of winning 講解

列出所有的可能性後你會發現，

if you switch than if you stay.

換門比不換門獲勝的機率更高。

It's easier to understand the problem if there are many more doors.

如果有很多扇門，這個問題就更容易理解了。

Say you chose one door out of a hundred.

假設你從100扇門中選擇了一扇。

The host then eliminates 98 doors

然後主持人排除了98扇

that they know don't have a prize behind them.

他們知道後面沒有獎品的門。

That leaves two doors,

那就只剩下兩扇門了，

the one you chose and the only other one remaining.

你選的那扇，以及剩下的唯一一扇。

Do you switch now?

你現在會換嗎？

Absolutely.

絕對會。

When you first picked,

當你第一次做出選擇時，

you only had a one in 100 chance of getting the right door.

你選對門的機率只有百分之一。

The odds of it being behind the other doors 文法

獎品在其他門後面的機率

was 99 out of a hundred.

是百分之九十九。

The host then filters out the options for you

然後主持人為你過濾了選項，

by eliminating 98 bad doors

剔除了98扇

that they know don't have the prize.

他們知道沒有獎品的錯誤之門。

This is to your advantage because it leaves the remaining door

這對你很有利，因為這讓剩下的一扇門

with the rest of the odds,

繼承了剩餘的所有機率，

a 99 out of a hundred chance of having the car.

也就是有百分之九十九的機率藏著汽車。

Some eventually admitted they were in the wrong. 慣用語

一些人最終承認他們錯了。

A team at the Massachusetts Institute of Technology worked on the problem

麻省理工學院的一個團隊研究了這個問題，

and afterwards Seth Kalson of MIT admitted,

之後麻省理工學院的賽斯·卡爾森承認：

"You are indeed correct.

「妳確實是對的。

My colleagues at work had a ball with this problem 慣用語

我的同事們為了這個問題討論得不亦樂乎，

and I dare say that most of them, 語氣意圖

而且我敢說，他們中的大多數人，

including me at first, thought you were wrong."

包括一開始的我，都認為妳錯了。」

To which she responded, 文法

對此她回應道：

"Thanks MIT, I needed that." 語氣意圖

「謝謝麻省理工，這正是我需要的。」

As for that math professor I mentioned earlier 表達脈絡

至於我前面提到的那位數學教授，

who sent that not so friendly letter,

也就是寄了那封不太友善信件的人，

Professor Sachs later conceded,

薩克斯教授後來妥協說：

"After removing my foot from my mouth, 慣用語

「在收回我那些愚蠢的話後，

I'm now eating humble pie. 慣用語

我現在正在虛心認錯。

I vowed as penance to answer all the people who wrote to castigate me.

我發誓要作為懲罰，回覆所有寫信批評我的人。

It's been an intense professional embarrassment."

這真是一次極度的職業尷尬。」

Our biggest misconception is assuming that two choices mean a 50-50 chance of something happening. 表達脈絡

我們最大的誤解在於認為兩個選擇就意味著事情發生的機率是50-50。

This makes sense if we don't have any other information.

如果我們沒有任何其他資訊，這是說得通的。

If I pick two people and ask who would win a tennis match

如果我挑了兩個人並問誰會贏得網球比賽，

and you don't know anything about them,

而你對他們一無所知，

you have a 50-50 shot of getting it right.

你猜對的機率就是50-50。

But if I said player A just took up the sport yesterday 片語動詞

但如果我說A選手昨天才開始接觸這項運動，

and player B has won Wimbledon,

而B選手贏過溫布頓網球錦標賽，

this would likely change your choice.

這很可能會改變你的選擇。

Information matters,

資訊至關重要，

just like when the game show host knew which door had a goat.

就像遊戲節目主持人知道哪扇門後有山羊一樣。

They weren't opening up a door randomly.

他們可不是隨機開門的。

So the more you know, 文法

所以你了解得越多，

the more informed decisions you can make.

你做出的決定就越明智。

Vos Savant once said,

沃斯·莎凡曾說：

"People that we think are very smart are not necessarily very smart." 文法

「我們認為很聰明的人不一定真的很聰明。」

She explained they're more likely to be educated or experienced rather than intelligent.

她解釋說，他們更有可能是受過良好教育或經驗豐富，而不是智力超群。

What does she think is holding people back from their intellectual potential? 片語動詞

她認為是什麼阻礙了人們發揮自己的智力潛能呢？

She's been critical of compulsory schooling

她一直對義務教育持批評態度，

because she says students learn passively.

因為她說學生們是在被動學習。

They sit there and are told what to believe

他們坐在那裡，被告知該相信什麼，

instead of learning to think independently.

而不是學習如何獨立思考。

She went so far as to say, 片語搭配

她甚至說過，

"I would rather not see compulsory schooling." 文法

「我寧願看不到義務教育。」

As for herself,

至於她自己，

she never graduated from university,

她從未從大學畢業，

dropping out of Washington University in St. Louis 片語動詞

在聖路易斯的華盛頓大學讀了兩年後便退學，

after two years to start a career in investment

開始從事投資行業，

before following her real passion, writing,

之後才追隨她真正的熱情——寫作，

leading to her famous answer to the problem

這也促成了她對那個難倒全世界的問題

that stumped the world. 慣用語

給出了著名的解答。

There's another way to learn that doesn't involve sitting in a classroom.

還有一種不需要坐在教室裡的學習方式。

Brilliant is an online interactive learning platform

Brilliant是一個線上互動學習平台，

that helps you brush up on your math, 片語動詞

能幫助你鞏固數學、

science, and computer science skills.

科學和電腦科學技能。

Speaking of the Monty Hall problem, 表達脈絡

說到蒙提霍爾問題，

my sponsor Brilliant has an entire course on probability,

我的贊助商Brilliant有一整套關於機率的課程，

which explores misconceptions that can arise,

其中探討了可能出現的誤解，

including that famous brain teaser. 片語搭配

包括那個著名的腦筋急轉彎。

If you're ever stuck, don't worry,

如果你卡住了，別擔心，

you can look at the explanation for more.

你可以查看解析了解更多。

There's something for everyone,

這裡有適合每個人的內容，

whether you're a beginner or simply want to improve on what you already know. 文法

無論你是初學者，還是只想在現有基礎上進一步提升。

You can solve puzzles with science through their scientific thinking course.

你可以透過他們的科學思維課程用科學知識解決難題。

One of my all-time favorites is their logic course,

我一直以來最喜歡的是他們的邏輯學課程，

which helps improve critical thinking that forms the basis of mathematical reasoning. 片語搭配

這有助於提高批判性思維，而這正是數學推理的基礎。

Brilliant is free for you to sign up by going to the custom link

透過點擊我的簡介或置頂留言中的專屬連結，

in my description or pinned comment,

你可以免費註冊Brilliant，

brilliant.org/newsthink.

網址是 brilliant.org/newsthink。

The first 200 people to use my link will get 20% off their premium membership,

前200名使用我連結的人將獲得高級會員20%的折扣，

which gives you access to all of their courses.

這樣你就可以訪問他們所有的課程。

Thanks for watching.

感謝觀看。

For NewsThink,

這裡是NewsThink，

I'm Cindy Pom.

我是Cindy Pom。