I'm Jeffrey Rosenthal.

我是傑弗裡-羅森塔爾。

I'm a professor of statistics at the University of Toronto.

我是多倫多大學的統計學教授。

And this is stats support.

而這是統計學上的支持。

That's been from King D.

那是來自國王D。

Web.

網絡。

Why do statisticians get so worked up over probability?

為什麼統計學家會對概率問題如此糾結？

Every event is just 50 50.

每項活動只需50 50。

It either happens or it doesn't.

它要麼發生，要麼不發生。

This is something I've heard before.

這是我以前聽說過的事情。

This idea that well if it can either happen or not it must be 50 50.

這種想法是，如果它要麼發生，要麼不發生，就一定是50 50。

Sometimes that's referred to by philosophers as the principle of indifference meaning that anything that could happen.

有時，這被哲學家稱為冷漠原則，意味著任何可能發生的事情。

They must all have the same probability.

他們必須都有相同的概率。

The thing is it's just not true.

問題是這不是真的。

When I go home today from the studio I might get killed by a bolt of lightning or I might not get killed by a bolt of lightning.

當我今天從工作室回家時，我可能會被一道閃電殺死，或者我可能不會被閃電殺死。

But I'm pretty sure there's not a 50% chance I'm going to get killed by a bolt of lightning.

但我很確定，我沒有50%的機會被閃電殺死。

Okay next we have a question from what the fuss who says why is statistics important in life really were awash in all kinds of different data.

好了，接下來我們有一個問題，誰說統計學在生活中為什麼重要，真的是被各種不同的數據所淹沒。

So anything from, you know the spread of disease or crime statistics or studies of a medical treatment or financial data or public opinion polls, there's so many facts and figures and statistics out there.

是以，任何事情，從，你知道疾病的傳播或犯罪統計或醫療研究或金融數據或民意調查，有這麼多的事實、數字和統計數字在那裡。

The science of statistics is a way to try to sort through it.

統計學的科學是一種試圖對其進行分類的方法。

So if you don't have any statistical knowledge or understanding or perspective then you're likely to say well this must be true because my friend said it or this must be true because I heard it on the news or I just kind of think it must be true.

是以，如果你沒有任何統計知識或理解或觀點，那麼你很可能會說這一定是真的，因為我的朋友說了，或者這一定是真的，因為我在新聞上聽到了，或者我只是覺得它一定是真的。

But if you have statistics you can try to analyze all the facts and figures that are out there and try to see what are the real trends, what's really happening versus what things really aren't the way people think they are next.

但是，如果你有統計數據，你可以嘗試分析所有的事實和數字，並嘗試看看什麼是真正的趨勢，什麼是真正的發生與什麼事情真的不是人們認為的那樣，接下來。

We have question from Lawrence I tv says question for statisticians, why did the polls get it so wrong explanations please.

我們有來自Lawrence Itv的問題，說是給統計學家的問題，為什麼民意調查會有這麼大的錯誤，請解釋一下。

Yeah.

是的。

So public opinion polling, especially when it's predicting elections is a very high profile thing, but also a hard thing to do and usually people notice the mistakes more than the corrections.

是以，民意調查，尤其是在預測選舉的時候，是一件非常引人注目的事情，但也是一件很難做的事情，通常人們注意到的是錯誤，而不是糾正。

So a lot of public polling for elections has actually been quite accurate and it's predicted things quite well.

是以，很多選舉的民意調查實際上是相當準確的，它對事情的預測相當好。

But there have been some high profile mrs for example the US presidential elections of 2016 and 2020.

但也有一些高調的夫人，例如2016年和2020年的美國總統選舉。

Now, even in those cases, typically the polls prediction compared to the actual results was usually only off by about four or 5%.

現在，即使在這些情況下，通常民意調查的預測與實際結果相比，通常只有大約4%或5%的偏差。

Which isn't such a huge amount considering how hard it is to figure out what's going to happen.

考慮到要想知道會發生什麼事有多難，這並不是一個巨大的數字。

But it's still a big enough error that if the election is closed, it can make a big difference.

但這仍然是一個足夠大的錯誤，如果選舉結束，它可以產生很大的影響。

So why is that?

那麼這是為什麼呢？

Well, election polls of course they don't ask everybody how they're going to vote.

好吧，選舉民意調查當然不會問每個人他們將如何投票。

They just ask a sample, usually a few 1000 people and then try to figure out what may be 100 million people are going to do.

他們只是問了一個樣本，通常是幾千人，然後試圖找出可能是1億人要做的事情。

So that is a challenge.

是以，這是一個挑戰。

The good news is if the polling is done randomly, that is were equally likely to pick every person with the same probability, then we have good statistics to allow us to figure out how accurate were going to be, what will be the so called margin of air, you know, how close will usually be to the true answer and actually that works pretty well.

好消息是，如果投票是隨機進行的，也就是說，我們同樣有可能以相同的概率挑選每個人，那麼我們就有很好的統計數據，讓我們能夠計算出我們的準確度有多高，所謂的空氣邊緣是什麼，你知道，通常會有多接近真實的答案，實際上這很有效。

But what makes it especially hard for the pollsters is that it's hard to get a random sample.

但讓民調機構特別難受的是，很難獲得隨機樣本。

And the main reason is because most people don't want to talk to pollsters, polling companies don't necessarily like to talk about it, but their response rates are usually less than 10% and that can lead to a lot of biases because maybe people who support a certain candidate are a little bit more likely to agree to talk to the pollsters than people who support another candidate.

主要原因是大多數人不願意和民調人員交談，民調公司不一定喜歡談論這個問題，但他們的迴應率通常低於10%，這可能導致很多偏見，因為也許支持某個候選人的人比支持另一個候選人的人更有可能同意與民調人員交談。

And any little response bias like that can have a huge impact on the results.

而任何像這樣的小反應偏差都會對結果產生巨大影響。

Question from common matt.

來自common matt的問題。

Think what are some common statistical errors and how can we learn to spot them and if possible correct them in others.

想一想，有哪些常見的統計錯誤，我們怎樣才能學會發現這些錯誤，並在可能的情況下糾正別人的錯誤。

And our own work, one of the biggest things is people don't think about what I like to call the out of how many principle and that's this idea that when something happens that striking people will compute the probability of it happening in that exact way to that exact person but not look at the chance that it will happen in some way to somebody.

我們自己的工作，最大的事情之一是人們不考慮我喜歡稱之為 "多少原則 "的東西，這就是這個想法，當事情發生時，引人注目的人們會計算它以那種確切的方式發生在那個確切的人身上的概率，但不看它會以某種方式發生在某人身上的機會。

There was a woman in England who had two sons, who each died in infancy, there is something as you probably know called SIDS or sudden infant death syndrome.

在英國有一個女人，她有兩個兒子，他們都在嬰兒期死亡，有一種你可能知道的東西叫SIDS或嬰兒猝死綜合症。

So maybe just two times she got really, really unlucky and her babies stop breathing or maybe she was a murderer and she'd actually, she actually suffocated them and she was actually arrested and charged and at her trial, they said, oh, it's so unlikely that there'll be two SIDS cases in the same family that we can rule that out.

是以，也許只是兩次，她真的很不走運，她的嬰兒停止了呼吸，或者也許她是一個凶手，她實際上，她實際上窒息了他們，她實際上被逮捕和指控，在她的審判中，他們說，哦，在同一個家庭中出現兩個SIDS病例的可能性很小，我們可以排除這個可能性。

She must have actually tried to kill them.

她一定是真的想殺了他們。

And that's an interesting example where if you just look at the probability given to kids in one family, what's the chance they're both going to die of SIDS?

這是一個有趣的例子，如果你只看一個家庭中孩子的概率，他們都死於SIDS的概率是多少？

Of course it is very unlikely.

當然，這是很不可能的。

But then if you say out of all the millions of families in the United Kingdom or in the whole world was a chance that somewhere, there's a family where two kids both died of SIDS extremely likely and it seems like that was the case with her.

但是，如果你說在英國或整個世界的所有數百萬個家庭中，有一個家庭的兩個孩子都死於嬰兒猝死症的可能性極大，似乎她就是這種情況。

There was actually no other evidence that she had actually tried to kill these kids.

實際上沒有其他證據表明她確實曾試圖殺害這些孩子。

He was just extremely unlucky and yet she was convicted, she was jail, she spent several years in jail before there was enough of an outcry and eventually on the second appeal the case was overturned question from josh Levs says, what's more likely than winning the lottery.

他只是非常不走運，但她卻被定罪了，她被關進了監獄，她在監獄裡呆了幾年，才有了足夠的呼聲，最終在第二次上訴時，案件被推翻了，來自Josh Levs的問題是，什麼比中彩票更有可能。

The short answer is everything that is to say if you're talking about winning a lottery jackpot for one of the big lotteries like mega millions or powerball, then the chance of winning that jackpot with a single ticket is one chance in a couple of 100 million depending on which lottery.

簡短的答案是一切，也就是說，如果你談論的是贏得彩票大獎的大彩票之一，如巨型百萬或強力球，那麼用一張彩票贏得大獎的機會是1億分之一的機會，取決於哪種彩票。

So just incredibly unlikely.

所以只是難以置信的不可能。

So compared to that, almost anything you can think of being killed by a bolt of lightning or the next person you meet will one day be the president of the United States or any crazy thing you can come up with.

是以，與此相比，幾乎所有你能想到的被一道閃電殺死或你遇到的下一個人有一天會成為美國總統或任何你能想到的瘋狂的事情。

We can estimate the odds for all of them and they're all more likely than the chance you're going to win the powerball lottery.

我們可以估計出所有這些的概率，它們都比你贏得強力球彩票的概率要大。

And in fact one that I like to use as an example is if you drive to the store to buy your lottery ticket, you're way more likely to be killed in a car crash on your way to the store than you are to win the jackpot.

事實上，我喜歡用一個例子，如果你開車去商店買彩票，你在去商店的路上被車撞死的可能性比你贏得大獎的可能性大。

Next we have a question from s mali mall, I'm just patiently waiting for people to realize that all statistics are skewed because the data is skewed in so many ways that I can't even list them all.

接下來我們有一個來自s mali mall的問題，我只是耐心地等待人們意識到所有的統計數據都是有偏差的，因為數據的偏差太多，我甚至無法一一列出。

So not a big fan of statistics maybe.

是以，也許不是一個統計學的大粉絲。

But that's true.

但這是事實。

There is that's a good point that all data is going to have some things that are wrong with it.

這是一個很好的觀點，所有的數據都會有一些錯誤的地方。

Maybe it was biased, maybe it wasn't measured correctly.

也許它是有偏見的，也許它沒有被正確測量。

Maybe it only shows part of the story, but I don't think that means we should just forget about it and just forget about statistics and data.

也許它只顯示了故事的一部分，但我不認為這意味著我們應該忘記它，只是忘記統計和數據。

Think what it means is we have to think carefully.

認為它的意思是我們必須仔細思考。

When we get data, we have to say how is this data collected?

當我們得到數據時，我們必須說這個數據是如何收集的？

Is it an accurate reflection of the truth?

它是否準確反映了真相？

In what ways is it going to be biased or misleading?

它在哪些方面會有偏見或誤導？

And then we can still draw inferences from it, but it's true that we have to be careful.

然後我們仍然可以從中得出推論，但我們確實要小心。

We have a question from john Friedberg says about to play what must be the absolute worst casino game in terms of play rods?

我們有一個問題，從約翰-弗裡德伯格說，關於玩什麼必須是絕對最糟糕的賭場遊戲，在玩棒子？

Any guesses?

有什麼猜測嗎？

Well, it's an interesting question.

嗯，這是個有趣的問題。

There's different casinos with different games, but one of the games, which to my surprise is one of the most popular and also has one of the worst odds against you is the video lottery terminals.

有不同的賭場，有不同的遊戲，但其中一個遊戲，令我驚訝的是，它是最受歡迎的遊戲之一，也是對你最不利的賠率之一，就是視頻彩票終端。

So people love them, but they usually have at least a 5% and maybe 10% or even 15% house edge.

是以，人們喜歡它們，但它們通常至少有5%，也許10%甚至15%的房子優勢。

So they're really not the best game.

所以他們真的不是最好的遊戲。

Now, there are some casino games which have odds which are much better for the player.

現在，有一些賭場遊戲的賠率對玩家來說要好得多。

So for example of the pure chance games, the game craps where you repeatedly roll a pair of dice kind of like these, you have a 49.2929% chance of winning.

是以，以純機會遊戲為例，在骰子游戲中，你反覆擲出一對像這樣的骰子，你有49.2929%的機會獲勝。

Next question from shave a cat.

下一個問題來自於剃光頭的貓。

See our murder rate skyrocketing or the media doesn't have much to report.

看到我們的謀殺率急劇上升，或者媒體沒有什麼可報道的。

So they are focusing more on that.

是以，他們更加關注這個問題。

That's a good question.

這是個好問題。

So murder rates have generally been coming down a little bit in the last couple of decades.

是以，在過去的幾十年裡，謀殺率一般都會有一些下降。

But in the last few years there's been a little bit of an uptick.

但是在過去的幾年裡，有一點上升。

So they're now a little bit higher than they were a few years ago, but they're still quite a bit lower than they were a decade or two ago.

是以，他們現在比幾年前要高一點，但比起十年或二十年前還是低了不少。

Also I've noticed for example politicians and police spokespeople and so on, they all will at times.

我還注意到，例如政治家和警察發言人等等，他們都會在某些時候。

Seo crime rates are way up for their own reasons.

Seo犯罪率一路上升，有其自身的原因。

They have reasons for wanting that to be said even though you know maybe it's not actually true.

他們有理由希望這樣說，儘管你知道也許這不是真的。

So it's just one more reason that if you want to know what's happening with something like, you know, rates of crime.

是以，這只是另一個原因，如果你想知道發生了什麼事，比如，你知道，犯罪率。

Well, don't listen to what a few people are saying.

好吧，不要聽信少數人的說法。

Look at the actual statistics and then you can see the truth.

看看實際的統計數據，然後你就能看到真相。

Next.

下一步。

We have a question from Brenda Clan says, how does probability work in the roulette?

我們有一個來自Brenda Clan的問題說，概率在輪盤賭中是如何運作的？

So it's a good question.

所以這是個好問題。

Rillettes are fairly simple.

煎餅是相當簡單的。

So the standard american roulette wheel has 38 of those little wedge slots and two of them are green, there's the zero and the double zero and then the others are divided into 18 red and 18 black.

是以，標準的美國輪盤有38個小楔形槽，其中兩個是綠色的，有零點和雙零點，然後其他的被分為18個紅色和18個黑色。

The person at the casino spins the wheel and presumably it's equally likely to come up any of those 38 different wedges.

賭場的人轉動轉盤，估計它同樣有可能出現這38個不同的楔子。

So what it means is if you bet on for example red, well 18 out of the 38 wedges are red, so you have an 18 out of 38 chance of getting red, which is a little bit less than 50%.

所以它的意思是，如果你賭紅色，那麼38個楔子中有18個是紅色，所以你有38箇中的18個機會得到紅色，這比50%要少一點。

And that's why if you bet on red, there's an even money payout, but on average you're gonna lose a little bit more money than you win.

這就是為什麼如果你賭紅色，會有雙倍的賠率，但平均來說你會輸的錢比贏的多一點。

You can also sometimes bet on different things like all the even numbers or something like that, but whichever bet you do, it works out to the same thing, there's a slight edge in favor of the casino and that's why if you play roulette over a long period of time, it's going to be more and more sure that you're going to lose more money than you win.

你有時也可以在不同的東西上下注，比如所有的偶數或類似的東西，但無論你做哪種下注，結果都是一樣的，有一個有利於賭場的輕微優勢，這就是為什麼如果你長期玩輪盤賭，會越來越確定你輸的錢比贏的多。

A question from Six latin six lover six, who makes betting odds.

一個來自Six latin six lover six的問題，他做了博彩賠率。

Is it an algorithm?

它是一種算法嗎？

So it's a really interesting problem for the bookies or the people who are making these odds.

是以，對於博彩公司或制定這些賠率的人來說，這是一個非常有趣的問題。

Now the goal is pretty easy to understand because if you're a bookie, what you want is pretty much to have the same amount of bedding on both sides.

現在的目標很容易理解，因為如果你是一個賭徒，你想要的是兩邊有相同數量的床上用品。

So that in the end you don't really care if the horse wins or not or you don't really care if the team wins or not because either way you're gonna make money because you're gonna get your cut, whereas if everybody bet on one side and then they all one then you could lose a lot of money.

是以，最終你並不真正關心馬是否贏了，或者你並不真正關心球隊是否贏了，因為無論如何你都會賺錢，因為你會得到你的抽成，而如果每個人都押在一方，然後他們都是一方，那麼你可能會損失很多錢。

But on the other hand how they do that is kind of a challenge and usually they're updating their odds as they go and if they say everybody's betting on this one team G we better change the odds so that the next bettors are more likely to bet on the other side and I'm not a bookie.

但另一方面，他們如何做到這一點是一種挑戰，通常他們在更新他們的賠率，如果他們說每個人都投注在這支球隊上，那麼我們最好改變賠率，這樣下一個投注者就更有可能投注在另一方，我不是一個賭徒。

But my impression is that in the old days it used to be on just kind of by their judgment or you know experience people looking things over and tweaking things.

但我的印象是，在過去的日子裡，它曾經是由他們的判斷或你知道的經驗的人看東西和調整的東西。

Whereas now there's so much online gambling that a lot of it is automated and they have algorithms which I think are not simple based on how everybody's betting and trying to adjust things.

而現在有這麼多的在線賭博，很多都是自動化的，他們有一些算法，我認為這些算法並不簡單，基於每個人的投注方式，試圖調整事情。

But the goal is pretty easy to understand.

但目標是相當容易理解的。

Trying to balance out those bets question from Zeno.

試圖平衡芝諾的那些賭注問題。

Notice what is a stochastic process really?

注意到什麼是真正的隨機過程？

Well, I'm glad you asked.

好吧，我很高興你問。

So stochastic is just another word for random.

是以，隨機性只是隨機的另一個詞。

So it means random processes or things that proceed randomly in time.

所以它意味著隨機過程或在時間上隨機進行的事物。

And the simplest example is actually one I sometimes like to illustrate with my students using a stuffed frog.

而最簡單的例子其實是我有時喜歡用一隻毛絨絨的青蛙來和我的學生說明的。

So I'll do that here and we imagine we have a frog which every second randomly decides either to move one step this way or to move one step this way and once it does then the next second it again decides randomly to move one step this way or one step this way.

所以我在這裡做一下，我們想象一下，我們有一隻青蛙，它每秒鐘都會隨機決定向這邊移動一步或向這邊移動一步，一旦它這樣做了，那麼下一秒鐘它又會隨機決定向這邊移動一步或向這邊移動一步。

And yet it's actually really interesting for mathematicians to study this.

然而，對於數學家來說，研究這個問題實際上是非常有趣的。

Once the chance that the frog will eventually return to where it started turns out it's 100% it's certain it might take a really long time, but eventually it's going to return to where it started and in fact eventually it's gonna be a million steps that way and eventually it's gonna be a billion steps that way, it's going to go to every single place.

一旦青蛙最終會回到它開始的地方的機會變成了100%，這是肯定的，它可能需要一個非常長的時間，但最終它會回到它開始的地方，事實上最終會有一百萬步，最終會有十億步，它會去到每一個地方。

Eventually.

最終。

If you wait long enough with probability one, we can prove that.

如果你用概率一等待足夠長的時間，我們可以證明這一點。

Next question from an S.

下一個問題來自一個S。

L.

L.

X.

X.

Says, what does it mean to be statistically significant?

說，統計學上的顯著性是什麼意思？

So statistically significant is saying probably it wasn't just chance that this is enough of an effect that we can pretty much you can never do it for sure.

是以，統計學上的顯著性是說可能這不僅僅是機會，這是一個足夠的影響，我們幾乎可以你永遠無法確定。

But you can pretty much say it's probably not due to chance alone.

但你基本可以說，這可能不僅僅是由於機會。

Probably this actually shows something real, there was really a difference or there was really an increase or something really happened.

可能這實際上顯示了一些真實的東西，真的有差別，或者真的有增加，或者真的有事情發生。

It wasn't just the random luck.

這不僅僅是隨機的運氣。

So the basic idea is pretty simple.

是以，基本的想法是非常簡單的。

It sometimes gets lost in the details.

它有時會在細節中丟失。

But when you notice something that happens, you know, maybe oh this classroom did better on the test than this other classroom then as statisticians, The fundamental question you're always asking is does that mean something real?

但是，當你注意到發生的事情時，你知道，也許哦，這個教室的考試成績比另一個教室好，那麼作為統計學家，你總是問的基本問題是，這是否意味著真正的東西？

Like, oh, maybe the teaching was better in this class or maybe people in that class are are are you smarter or was it just random luck.

比如，哦，也許這個班的教學更好，或者也許那個班的人更聰明，或者這只是隨機的運氣。

So you'd never expect any two results to be exactly the same.

所以你永遠不會期望任何兩個結果完全相同。

There's always going to be some differences.

總是會有一些差異。

Okay, next question from john l worthy, can someone please help with this?

好的，下一個問題來自John L worthy，誰能幫助解決這個問題？

One of the odds of having three generations of family members being born on the same day.

有三代家庭成員在同一天出生的機率之一。

First was born on January 10, 1943, the second same day, 1994 and the third same day in, in 2022.

第一個生於1943年1月10日，第二個同一天，1994年，第三個同一天在，2022年。

It's actually a good example of the sort of question that there's different ways of looking at the probability.

這其實是一個很好的例子，這種問題有不同的方式來看待概率。

So if you just say there's three people, what are the chances that all have been born on the same day?

那麼，如果你只是說有三個人，所有的人都在同一天出生的可能性有多大？

Well, that's pretty straightforward.

嗯，這是很直接的。

You can think, well, the first one could be born on any day.

你可以想，嗯，第一個人可以在任何一天出生。

It doesn't really matter.

這其實並不重要。

Then the second one has roughly one chance in 365 of being born on that same day.

那麼第二個人大約有365分之一的機會在同一天出生。

And then the third one has roughly one chance in 365 of being born again on that same day.

然後第三個人大約有365分之一的機會在同一天重生。

So it's one chance in 365 times 365, which was that a little less than one chance in 100,000 I think.

是以，這是365分之一的機會乘以365，這比我認為的10萬分之一的機會要少一點。

So it's quite unlikely.

所以這是很不可能的。

One way I'd like to look at these kind of questions is this is sort of out of how many different ways that this could have happened.

我想看一下這類問題的一個方法是，這是在可能發生的多少種不同方式中的一種。

So even in this one family probably there's a lot of other people in each of those generations and if any three of them had matched up their birthdays then this the same tweet could have been written.