WAYC Lesson 2 - Prize Madness!

​Prize Madness!

Multiple Choice

What is probability?

• A ratio comparing the chance or likelihood of an event occuring.

• A ratio comparing how much of an event occurs.

• A number that shows I'm smart.

• Something that is going to be happening.

Fill in the Blanks

Theoretical probability is the

chance that an event will occur.

Fill in the Blanks

Experimental probability is the probability of something based on the results of several

Math Response

If I flip a coin, what is the probability that it lands on heads?

Type answer here

Correct Answer: \frac{1}{2}

Deg^°

Rad

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.

Open Ended

Predict the chances that you will win a prize. If we run this experiment 20 times, how many times can you expect to win a prize?

Draw

Let's conduct this experiment 20 times. Record the number of blue and red cubes drawn in the chart.

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?

Draw

Let's conduct this experiment 20 more times. Record the number of blue and red cubes drawn in the chart.

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.

Open Ended

Alex conducted the Prize Madness activity six times and got 3 red cubes and 3 blue cubes. His friend Ling Ling said that Alex must have done something wrong because these events were not equally likely to occur. Alex knows he did nothing wrong but wasn't sure how his results could have happened. Explain to Alex and Ling Ling why it is possible to get Alex's results.

​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...

Let's Back Up a Second...

​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?

Draw

Run the modified Prize Madness experiment 20 times. Record the results on the chart.

​What Happened?

How did our probability change?

Did it become more even?

Open Ended

How could you place 2 red blocks and 2 blue blocks into 2 bags that would allow for the blue cubes to be chosen MORE than the red cubes?