Let me do this once again.

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

All of the equally likely events.

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

Let's toss up for it.

Let's decide by coin toss.

Could I see the quarter?

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

And then, 1 of the coins is a two sided head coin.

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.

There's 3 different things happening.

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

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.

Let me now flip that coin once, and I want you to tell me, what's the probability that this coin which could be 50 chance fair coin and 50 chance a loaded coin.

So once again, we can't call them equally likely events.

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

I need, Don Corleone, those politicians you are carrying in your pocket.

But that's the easy part.

Here we have our first sample.

Anyway, let's say I'm going to now flip a coin twice.

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

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

Check all that apply. Also, assume that the probability of heads is neither 0 or 1.

With the Central Limit Theorem, things become really easy.

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

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.

So let's say I have a bag full of coins.

We have a bag filled with coins. Each of these coins maybe a bit different.

This is the expression over here. Let's practice this one last time.

Fair coins always come up 50 heads or tails.

There is a solution. The solution is to fake it or more precisely to add fake data.

So s is equal to 84 feet.

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.

Suppose I flip a coin, and the coin comes up tails or heads.

So we could say in general, that the probability of me getting 5 out of 5 coins, given that I got a normal coin times the probability that I got the normal coin that is going to be equal that 5 out of 5 happens and I got the normal.

Well, there are 9 normal coins out of the 10 equally

Let's assume there are two coins equally distributed, same probability of having each.

So what's the probability that I get a normal coin?

P of fair is one and so P of flips given fair is always going to be equal to

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.

She picked up a coin.

My hobby is collecting coins.