Analyzing Compound Events

Focus Questions:

• How can you decide if a game is fair or not?
• How can we determine the theoretical probability of a compound event?

New Vocabulary:

• Fair Game - a game where the winning and losing are "equally likely"
• Sample Space - a list of all of the possible outcomes for an event.
• Tree Diagram - One type of "sample space" that is useful for events that have more than two parts.
• Compound Event - An event that has two or more parts or actions

Part 1: The Coin Game

Here are the rules of this game:

• You will toss three coins.
• If all three of the coins match, you get a point (and some money).
• If all three of the coins do NOT match, I get a point.
• Everybody gets one turn.
• At the end, the team (students or teacher) with the most points wins.

Part 2: Analzying the Game

1. What is the "experimental probability" of having all three coins match?
2. How many outcomes are there in this game?
3. Draw a sample space to determine all of the outcomes. (which type of sample space should you draw?)
4. Is this a "fair game"? Explain why or why not.

Part 3: The Bonus Prize

You are a contestant on Gee Whiz Everybody Wins and have made it to the final "Bonus Round".  In the Bonus Round you get to choose one of two games to play.

Game #1

• How to Play - Choose a block from Bag #1 THEN Choose from Bag #2
• How to Win - If you correctly predict the color of block that you will choose from each bag, you win.

Game #2

• How to Play - Choose a block from Bag #1 AND Bag #2 at the same time.
• How to Win - If you correctly predict the color combination that you will choose, you win.

Which game should you play?  Justify your decision with experimental and theoretical probabilities.

Part 4: Playing The Game

Task A:

• Run each experiment 18 times.  Record the results in your table.  Please remember to treat the bags kindly as they need to be used in multiple classes.
• After you have completed your experiment, fill out the forms below to contribute to class data.
• Game #1
• Game #2
• Here are the results from our class data: 

Part 5: Analyzing the Experiment

Answer the following questions in your squarebook:

1. What is the "experimental probability" of choosing each outcome for Game #1? Game #2?
2. What is the "theoretical probability" of choosing each outcome for Game #1? Game #2?
3. Are all of the outcomes "equally likely" for Game #1? Game #2?
4. How do the "experimental probabilities" and the"theoretical probabilities" compare for Game #1? Game #2?
5. Which Game should you choose to play? What should you predict if you play this game?

By the end of this lesson, you should be able to do the following:

• Determine whether a game is "fair".
• Describe how a "compound event" is different from a "simple event"
• Determine the "sample space" for a compound event using a probability tool such as a tree diagram or table

Homework:

1. ACE (9,11,12) (26) (*38)
2. Mid-Unit Summative on Investigations 1 and 2 next class.