WAYC Lesson 2 - Prize Madness!

Let's Play a Game

I have two bags. Inside one of the bags is a single red cube. The other bag has 3 red cubes, and 4 blue cubes.

You flip a coin to see which bag you will choose from.

If you select a red cube, you do not win. If you select a blue cube, you win!

Mr. V will give you a prize if you win.

Let's Review...

What did you notice about the results?

What is the probability of winning?

What is the probability of losing?

How are they related?

Checking In...

How did our second set of results differ from our first set of results?

What would happen to our chances if we added them together?

What if we did this 140 more times? What would happen to our chances?

The Law of Large Numbers

The experimental probabilities collected over many trials will predict the theoretical probabilities only when a very large number of trials are conducted.

The greater the number of trials, the closer to the experimental probability is to the theoretical probability.

​Let's Back Up a Second...

If I add the probability of something happening with the probability that same thing doesn't happen, what will my answer be?

The answer you should get is...

​1!

The sum of all probabilities of all outcomes of an experiment is always 1.

Think of it as this: if you account for all possibilities, then the event is certain to happen, which is a probability of 1.

​Let's Try It Again...

But this time, let's change the parameters.

Let's do the original experiment again, except each bag will contain two red cubes and two blue cubes.

What are your predictions?

​What Happened?

How did our probability change?

Did it become more even?