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.

(Applause)

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

Yeah. I need rug marbles. I know.

Now, one thing I will let you think about is

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

The bag is not transparent

So two of them satisfy your criteria.

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.

We have one, two, three yellow marbles.

We have two green marbles one, two green marbles.

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

And he literally sticks them into the empty bag

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

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

We have two red marbles.

And then there's one blue marble.

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

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

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

So let me draw them.

Three of them satisfy your conditions.

Three of them would be a yellow marble.

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

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.

Well, the total possible outcomes

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.

Then you're going to win the prize of

So when you take that second pick, the number of green marbles that are in the bag depends on what you got on the first pick.

And if you're able to pick two green marbles

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

And so over here, each book and each world becomes a little marble that I drag in to this magical device within the device.

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.

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

But the realization here is what you do with that first green marble.

We was talking about old school mc's and battles and stuff

The symbols.

Bee?

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

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.

Dependent on the first pick.