That's important, right?

So we did a little research we discovered on average Tim Hortons cells about three million coffees every day.

So say per day.

Okay, now, probably dream rope the rim.

That's probably actually a little bit higher, because this is probably taken from an average over the year or something.

But we'll just take these numbers to make it simpler for us.

So they sell three million coffee today, and we know that rule the rim we researched again for this year, which was 2013.

It started on Fed, I think 18 and went to March 17.

Okay, so that's a month, which is four weeks.

Okay, so four weeks, we've got to convert it two days time, seven days a week.

It is going to give us What is that?

28 28 days.

So this event of rolled to room last for 28 days may sell three million coffees per day.

Okay, Now the discrepancies in probability a lot of times they tell you that you have what, a one in six chance of winning, says right, One in six chance of winning.

But many people, well, by nine coffees and not win anything where you said you've won five times.

And when we bought, like, maybe 10.

10.

Yeah.

So you're doing way better than what the probability is, where other people are doing Terrible compared to that probability.

Well, let's tryto make sense of this using empirical probability, which we talk about, and law of large numbers and then theoretical probability.

So the idea here is let's try to actually calculate how many coffees are winners in this case.

So assuming that they're selling three million coffees a day over the course of 28 days, we're gonna multiply these two numbers.

Okay, so three million.

So this is gonna be the amount of coffees they sell, so they sell three million, a very large amount over the course of 28 days.

Okay, so we're gonna multiply that, and I'll just take a calculator out to make this a little simpler.

So we're estimating that they sell well.

She had calm is here, but it looks like 84 million.

Yeah, So looks like over the course of this, they're gonna sell 84 million coffees.

Okay, So in other words, that's the total amount of coffees they sell.

So what we're gonna do is kind of convert this fraction.

They've given us their telling us we have a one in six chance.

Well, what they did is they reduced a fraction.

So they had a one in six chance, but six being thinking of our total number.

Right?

So this is our theoretical probability.

And this is through what Tim Hortons is probably made through coffee.

So they actually sell 84 1,000,000 coffees were gonna calculate how many coffees air, actually, winners in this case, we're gonna figure out what this value is here.

Well, in order to do this because their equivalent fractions, we need to multiply this by some.

Number two get to 84 mil.

And the best way to figure out is actually just take any four million and divide by six.

And that'll tell us what this number is that we multiply and then we'll have to multiply the number on talk by that same value to figure this out.

Okay, so that's just, um, a couple steps.

So Avery, four million.

We divided by six.

It looks like 14 million is the number they multiplied by.

Okay, I'll write it down here.

They multiplied by 14 million.

When?

What is one times 14 million forties.

So, in other words, there are 14 million winning cups.

That's importance.

Great.

Okay, that makes sense.

But let's try to think about this in terms of practicality.

Okay, so in theory, this is our fear radical.

Make sure you spell that, right?

Great.

Yes.

Okay.

So if you're radical, you took Cole Probability.

They say you have a one in six chance of winning.

Right?

Okay, well, we'll use some empirical probability.

Let's say you're the person buying coffees, so we're gonna use this information we have here.

Okay, So we're gonna do some empirical, probably.

And what that is is doing the testing herself.

So let's say you are the person who buys all the coffee symptoms hands.

So in the end, how many coffees are you gonna buy If you buy all of them?

Drink role for a four million.

OK, so you've bought 84 million in the end, okay?

And this is leads us to our love large numbers, and that's that what they call in your book.

L l love large numbers.

Okay, well, let's say you start with the first coffee you buy, and you have your options of either you win or you looks right.

Well, let's say we we went on the first coffee by great.

Okay, We want.

And then on the next coffee we buy.

So coffee number two, we lose.

And then coffee number three, we lose coffee.

Four, We lose coffee.

Five Release Copy.

Six.

We lose seven.

I'm gonna go eight and then nine.

Okay?

So I'm gonna say this.

That just happens.

Okay?

Let's just say that happens just because I'm sure many people have found this right.

They start with the first coffee, and then they lose, lose, lose, lose.

Lose.

Well, up to this point, they want nine coffees.

Okay, so we're gonna talk about the relative frequency of each of these.

Okay?

So I'm just gonna put a little line on top to help us determine the relative frequency.

We'll call that will do that.

So Negative frequents.

Okay, well, in the 1st 1 how many coffees have you bought?

One.

And how many times, if you want.

So In the short term, it looks like you're 100% chance of winning, which is ridiculous, right?

Well, that's not how this thing.

And then the second time we buy coffee, what happens?

Uh, well, we don't win, but how many wins have do we have?

01 Okay, so we have one out of two coffees.

So now all right away.

We've dropped to 0.5 or known as 50% and it looks like we end up losing the rest of the time.

Right?

So this is out of the third, the fourth, the fifth, the sixth, the seventh, the eighth.

And then then Then I have coffee.

Well, because we only chose one win.

In this case, our probability continuously decreases.

It looks like when we're taking our dad, but eventually, what's gonna happen is because we talked about the probability being one in six and this is kind of the one we were talking about.

That one in six.

That's the probability.

In the end.

Um, what's gonna happen is we change.

These wind loses.

I'm just gonna change the way we set this up now.

So this is great for what we had.

Um let's say that we instead put this as a percentage, okay?

And because probability goes at the highest is one, and the lowest is zero.

We'll call.

This was 0.5.

Okay, this will have to change now, see, if we want in our first coffee, we're at probably have 100%.

Then if we lose on the second coffee, well, then we're one attitude, which is 50%.

Okay, So I'm just gonna change the Easter values now, because before that was just for winning and losing, right?

We're at 50%.

Well, when we're 1/3 1 in one out of three coffees were down too.

33.3%.

If we divide one divided by three.

Okay.

And then 1/4 of coffees.

We're going down to 25th and then it keeps going down, but eventually.

So in this case, it goes down down, down 1/9 of the chance of winning.

But as we get up, it's gonna pick up again, right?

And because this says it has a one in six chance, we're gonna find out what that value really is.

I think one divided by 6 16% So 16% is.

Well, say there, and we'll draw a line across to help us.

Dude and blue draw a line across.

So here we go.

There's a line of 16% as we buy more more coffees.

Okay, what's gonna happen is maybe in this course, we're going to get closer and closer to the line, maybe jump above it and below it, and then we go below again.

Then we go up, we win a lot and we go down by the time we get to our 84th 1,000,000 we should be on that value if we bought all the coffee's.

Okay, So this is empirical.

This is from buying all of the coffees and finding the relative frequents.

And we stumble around that line because importance tell us we have a 0.1 in six chance.

So what we discovered, okay.

And this kind of helps play into, um, the real life when we did the real life value on our 1st 9 coffees, we only won once, which is not a one in six chance.

It was only a one in nine chance.

But because of the law of large numbers, the more we buy eventually because we discussed how two moons has 14 million winning cups.

Eventually we start buying winning cups, and then we maybe, you know, jump above it, go back below, depending on which cups and we stay up for a bit.

But eventually we're gonna end up right on that 0.16 Okay, that's the probability of winning at Tim Hortons.

Okay, so why does this event happen?

Why do some people win a lot and some people lose a lot?

Well, you already figured out there was a total of 84 million coffees, right?

84 million coffees.

How many were winners?

We said 14 million were winners.

That's right.

Which means how many losing coffees are there?

Eight before divide not divided by but so track.

Sorry as a trap.

That's what's attracting is too.

What are we getting it for?

Losing coffees?

Because losers attract these numbers.

This become zero, so 70 there are 70 million losing cups of coffee.

Okay, so that means over the course of our empirical data, here 100 skip it when we're buying or 84,000,070 million times.

We had to buy a losing cup.

So when we only by nine cups?

Well, yes, 70 million or losing cup.

There's a great chance we buy a bunch of losing cups to start right?

That's the idea of you not actually meeting there one in six off the beginning, but eventually you'll buy up.

We could say eventually you buy up all the 70 million cups, and then they're only left with winning cups if you pop in the purchase in that way.

So you had horrible, horrible luck to start.

You buy all 70 million cups to lose to start.

Well, then what's left is the 14 million.

But that's why some people might not experience success in the short term, right?

And I think they call that in your book.

Um, we'll have to do it the law of large numbers.

But just because it's a one in six chance, it doesn't mean in the short term, every time you buy your six cup, you're gonna win your animal sticks, you win.

It just means that overall, in the 84 million that we guess that's him holding cells that there is what in six of those 14 million of those are raining cups, but it's still a great chance you grab losing cups.

Is there 70 million losing cups of coffee in that case?

So it is very likely that you do grab that stuff right there, just saying overall.

So I think that kind of sums up the whole Aviles ideas there.

Well, just like what?

I just said that because I was a good point.

So because where you're kind of fuse on how this Kraftwerk So assume in a bit.

Let's talk about so again, what we're doing here is we're figuring out our percentages, right?

So we want our 1st 11 which really represents 100% right 100% in time.

Well, then you lost the next time, so you dropped to 50% of the time.

You're waiting.

That's your relative frequency of wins.

Then this dropped 2.33 which is one divided by 31 divided by four is 40.25 divided by 5.21 Divided by six is right on our 1 16 Right.

Which is exactly what theoretically we should be getting for then, you know, we buy our seventh cup.

We lost, We drop below eight, we drop below nine.

We drop below, and then we buy our other 83 million here and maybe eventually to go up down below.

But in the end, there's 14 million winners If I bought them all now, the law of large numbers nine cups is not large.

So it would have been actually legitimate to say that you had zero winners in nine cups because nine compared to 84 million is not a large adopted all.

Remember, there are 70 million losing cups versus the 14 million, so it doesn't mean that the theoretical probability is wrong.

It just means that you haven't taken enough empirical data to get up to that fear radical.