Let me do this once again.

Is that the coin? The coin?

She took coins from the fontana?

Stacy... I need the coins.

What could you possibly want with those?

Like a coin? No.

This time around, we have a bag, and in the bag are 2 coins,coin 1 and coin 2.

So let's ask an easy quiz. Suppose we do 2 coin flips.

But that's the easy part.

Here we have our first sample.

The first coin flip might also come up tails, in which case I pick a very different coin.

Note that the 0.5 simply represents that there's an equal or 50 chance of having coin 1 versus coin 2.

The coin.

Are you a coin collector?

With the Central Limit Theorem, things become really easy.

Dan Jurafsky Does Lufthansa serve breakfast and San Jose? Well, that sounds funny.

And it is equal to well, this is one that we covered in the last video.

Random variables are really ways to map outcomes of random processes to numbers

another sheep for 50, you can have more than 1.

you wanna flip a coin to see who leads?

You'd leave a man's life to chance?

The probability that I got 5 out of 5 heads, given the two sided coin times the probability of the two sided coin b we defined event b as the two sided coin.

Let's go back to probability and go back to our simplest of all examples that of a coin flip.

And this expression equals 0.6080 and so the probability that we have the same coin is simply the probability that we both have type 1 or fair coins, plus the probability of my having coin 2 times the probability of your having coin 2.

All of the equally likely events.

Liz... have you got a quid?

My 18month chip.

Change, I mean. Coins.

The tails side is very nice.

This is going to be equal to the probability that you get 5 out of 5 heads given let's call that a normal coin given a normal coin times the probability that you had a normal coin times the probability of

We ask the probability what are the chance it comes up heads k times.

Here's what I'm going to do. I'm going to grab a random coin with 50 chance.

She picked up a coin.

So here's the scene for the first question I'm going to ask you.

learn in this video.

Here's the game tree for another stochastic game.

Gather them.

Do you want the coin back?

Quickly, give me the following numbers of the probability of coming up tails for coin 1 and for coin 2.

So now what happens is, I'm going to remove one of the coins from this bag, and each coin, coin 1 or coin 2, is being picked with equal probability.

And here is my answer. You can really read off the formula that I just gave you.

What's the probability of getting let's say I were to flip a coin seven times.

Take a coin flip. There is a true probability p for the coin.

Let's toss up for it.

Let's decide by coin toss.