I'm Jeffrey Rosenthal.

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

And this is stats support.

That's been from King D.

Web.

Why do statisticians get so worked up over probability?

Every event is just 50 50.

It either happens or it doesn't.

This is something I've heard before.

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

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

They must all have the same probability.

The thing is it's just not true.

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.

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

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.

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.

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

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.

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.

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

Yeah.

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.

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

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

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

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

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

So why is that?

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

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.

So that is a challenge.

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.

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

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.

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

Question from common matt.

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

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.

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.

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.

She must have actually tried to kill them.

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?

Of course it is very unlikely.

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.

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

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.

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.

So just incredibly unlikely.

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.

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.

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.

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.

So not a big fan of statistics maybe.

But that's true.

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

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

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.

Think what it means is we have to think carefully.

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

Is it an accurate reflection of the truth?

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

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

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

Any guesses?

Well, it's an interesting question.

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.

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

So they're really not the best game.

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

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.

Next question from shave a cat.

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

So they are focusing more on that.

That's a good question.

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

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

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.

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

Seo crime rates are way up for their own reasons.

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

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

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

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

Next.

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

So it's a good question.

Rillettes are fairly simple.

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.

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

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%.

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.

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.

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

Is it an algorithm?

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

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.

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.

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.

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.

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.

But the goal is pretty easy to understand.

Trying to balance out those bets question from Zeno.

Notice what is a stochastic process really?

Well, I'm glad you asked.

So stochastic is just another word for random.

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

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

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.

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

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.

Eventually.

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

Next question from an S.

L.

X.

Says, what does it mean to be statistically significant?

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.

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

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

It wasn't just the random luck.

So the basic idea is pretty simple.

It sometimes gets lost in the details.

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?

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.

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

There's always going to be some differences.

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

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

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

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

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

Well, that's pretty straightforward.

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

It doesn't really matter.

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

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

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

So it's quite unlikely.

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.

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.

So right away the chances a lot bigger because there's lots of different combinations which all could have led to the same conclusion.

It's not incredible that it happens but it's still pretty cool when it does happen to you from A J.