Let's do a couple of excercises from our probability one module. We have a bag with nine red marbles, two blue marbles, and three green marbles in it.

Yeah. I need rug marbles. I know.

One, two, three, four, five, six, seven, eight, nine red marbles. That looks some kind of orangesh but does the job. Two blue marbles.

Now, one thing I will let you think about is

The bag is not transparent

So two of them satisfy your criteria.

So we have one, two red marbles, assuming they're all mixed in there.

And he literally sticks them into the empty bag

Now you have one less marble in the bag and we're assuming that the first pick was green

(Applause)

We have one, two, three yellow marbles.

So let me draw them.

And Leibniz was the first person to really talk about building such a machine.

So first of all, what's the probability that the first marble you pick is green?

Three of them satisfy your conditions.

Three of them would be a yellow marble.

Then you can pretend they're marbles and you're a hungry, hungry... hungry hippo.

And you walk up to a table, and on that table there is an empty bag and the guy who runs the table says, Look, I've got some marbles here, three green marbles, two orange marbles, and I'm gonna stick them in the bag

We have two green marbles one, two green marbles.

And remember our constraint is selecting a non blue marble from the bag.

We have two red marbles.

And then there's one blue marble.

Feel around the marbles, all the marbles feel exactly the same

Then you're going to win the prize of

Well, the total possible outcomes

So the probability of picking a yellow marble is 3 8.

Now look inside the blueberry, and blow it up to the size of a football stadium, and now the nucleus is a marble in the middle.

He talked about doing it with marbles, having gates and what we now call shift registers, where you shift the gates, drop the marbles down the tracks.

So let's just think about this bag a little bit.

Seems like a pretty straight forward thing.

Or we could write that as zero point three zero

So there's a total number of eight balls.

You don't take that first green marble out, look at it, and put it back in the bag.

How many different possible marbles can we take out? There are one, two, three, four, five, six, seven, eight, nine , ten, eleven, twelve, thirteen, fourteen possible marbles.

So we have one blue marble. Two blue marbles. And then we have three green marbles.

That looks like a vase. We have nine red marbles. So we draw nine red marbles.

Three green marbles. Let me draw those three...One, two, three.

And they want to know the probability of pulling a yellow marble.

If the first pick is green, then you don't have three green marbles in a bag of five

Find the probability of pulling a yellow marble from a bag with three yellow, two red, two green, and one blue marbles, I'm assuming.

Well we drew this scenario right over here

The symbols.

Bee?

Well there's a couple of ways of think about it.

And if you're able to pick two green marbles