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

(Applause)

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

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 one, two, three yellow marbles.

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

So let me draw them.

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.

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.

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.

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.

Well, the total possible outcomes

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

Then you're going to win the prize of

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 the probability of picking a yellow marble is 3 8.

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

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 there's a total number of eight balls.

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.

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

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

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.

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

And if you're able to pick two green marbles

Well we drew this scenario right over here

Mr Bee,