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What I want to do in this video is

give you at least a basic overview of probability.

Probability, a word that you've probably heard a lot of.

and you are probably just a little bit familiar with it

Hopefully this will get you a little deeper understanding.

So let's say that I have a fair coin over here.

When I talk about a fair coin

I mean that it has an equal chance of

landing on one side or another.

So, you can maybe view it as the sides are equal,

the weight is the same on either side,

if I flip it in the air,

it's not more likely to land on one side or the other;

it's equally likely.

And so you have one side of this coin

So this would be the heads, I guess.

trying to draw George Washington

I'll assume it's a quarter of some kind

And then the other side, of course, is the tails

So that is heads,

and the other side right over here is tails.

And so if I were to ask you,

"What is the probability?"

I am going to flip a coin,

and I want to know

What is the probability of getting heads?

And I could write that like this

The probability of getting heads

And you probably, just based on that question

Have a sense of what probability is asking

It's asking for some type of way

of getting your hands around in an event

that's fundamentally random

We don't know whether it's heads or tails,

but we can start to describe the chances of it

being heads or tails.

And we'll talk about different ways of describing that.

So one way to think about it

And this is the way

that probability tends to be introduced in textbooks.

Is you say, well look,

how many different equally likely possibilities are there.

So how many equally likely possibilities

So number of equally likely possibilities

And of the number of equally possibilities,

I care about the number that contains my event right here.

So the number of possibilities

that meet my constraint,

that meet my conditions.

So in the case of the probability of figuring out heads,

what is the number of equally likely possibilities?

Well, there's only two possibilities

We're assuming that the coin can't land on its corner

and just stand straight up

We're assuming that it lands flat.

So there's two possibilities here,

two equally likely possibilities.

You could either get heads, or you could get tails.

And what's the number of possibilities

that meet my conditions?

Well there's only one condition of heads

So it'll be one over two

So one way to think about it is the probability

of getting heads is equal to one over two

is equal to one half.

If I wanted to write that as a percentage,

we know that one half is the same thing as fifty percent.

Now, another way to think about

or conceptualize probability,

that will give you this exact same answer,

is to say well if I were to run

the experiment of flipping a coin, so this flip,

you view this as an experiment

I know this isn't the kind of experiment that

you're used to, you know, you only think

an experiment is doing something with,

in chemistry or physics or all the rest,

but an experiment is every time you run this random event

So one way to think about probability is

if I were to do this experiment

An experiment many, many, many times

If I were to do it a thousand times or a million times

or a billion times or a trillion times

And the more, the better

give you at least a basic overview of probability.

Probability, a word that you've probably heard a lot of.

and you are probably just a little bit familiar with it

Hopefully this will get you a little deeper understanding.

So let's say that I have a fair coin over here.

When I talk about a fair coin

I mean that it has an equal chance of

landing on one side or another.

So, you can maybe view it as the sides are equal,

the weight is the same on either side,

if I flip it in the air,

it's not more likely to land on one side or the other;

it's equally likely.

And so you have one side of this coin

So this would be the heads, I guess.

trying to draw George Washington

I'll assume it's a quarter of some kind

And then the other side, of course, is the tails

So that is heads,

and the other side right over here is tails.

And so if I were to ask you,

"What is the probability?"

I am going to flip a coin,

and I want to know

What is the probability of getting heads?

And I could write that like this

The probability of getting heads

And you probably, just based on that question

Have a sense of what probability is asking

It's asking for some type of way

of getting your hands around in an event

that's fundamentally random

We don't know whether it's heads or tails,

but we can start to describe the chances of it

being heads or tails.

And we'll talk about different ways of describing that.

So one way to think about it

And this is the way

that probability tends to be introduced in textbooks.

Is you say, well look,

how many different equally likely possibilities are there.

So how many equally likely possibilities

So number of equally likely possibilities

And of the number of equally possibilities,

I care about the number that contains my event right here.

So the number of possibilities

that meet my constraint,

that meet my conditions.

So in the case of the probability of figuring out heads,

what is the number of equally likely possibilities?

Well, there's only two possibilities

We're assuming that the coin can't land on its corner

and just stand straight up

We're assuming that it lands flat.

So there's two possibilities here,

two equally likely possibilities.

You could either get heads, or you could get tails.

And what's the number of possibilities

that meet my conditions?

Well there's only one condition of heads

So it'll be one over two

So one way to think about it is the probability

of getting heads is equal to one over two

is equal to one half.

If I wanted to write that as a percentage,

we know that one half is the same thing as fifty percent.

Now, another way to think about

or conceptualize probability,

that will give you this exact same answer,

is to say well if I were to run

the experiment of flipping a coin, so this flip,

you view this as an experiment

I know this isn't the kind of experiment that

you're used to, you know, you only think

an experiment is doing something with,

in chemistry or physics or all the rest,

but an experiment is every time you run this random event

So one way to think about probability is

if I were to do this experiment

An experiment many, many, many times

If I were to do it a thousand times or a million times

or a billion times or a trillion times

And the more, the better

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