Comparing Estimated Probabilities to Probabilities Predicted by a Model

Examples, videos, and solutions to help Grade 7 students learn how to compare estimated probabilities to those predicted by a probability model.

New York State Common Core Math Grade 7, Module 5, Lesson 9

Worksheets for Grade 7

Lesson 9 Student Outcomes

• Students compare estimated probabilities to those predicted by a probability model.

Lesson 9 Summary

• The long-run relative frequencies can be used as estimated probabilities of events.
  
• Collecting data on a game or chance experiment is one way to estimate the probability of an outcome.
  
• The more data collected on the outcomes from a game or chance experiment, the closer the estimates of the probabilities are likely to be the actual probabilities.

Lesson 9 Classwork
Game Show—Picking Blue!
Imagine, for a moment, the following situation: You and your classmates are contestants on a quiz show called Picking Blue! There are two bags in front of you, Bag A and Bag B. Each bag contains red and blue chips. You are told that one of the bags has exactly the same number of blue chips as red chips. But you are told nothing about the number of blue and red chips in the second bag.

Each student in your class will be asked to select either Bag A or Bag B. Starting with Bag A, a chip is randomly selected from the bag. If a blue chip is drawn, all of the students in your class who selected Bag A win a Blue Token. The chip is put back in the bag. After mixing up the chips in the bag, another chip is randomly selected from the bag. If the chip is blue, the students who picked Bag A win another Blue Token. After the chip is placed back into the bag, the process continues until a red chip is picked. When a red chip is picked, the game moves to Bag B. A chip from the Bag B is then randomly selected. If it is blue, all of the students who selected Bag B win a Blue Token. But if the chip is red, the game is over. Just like for Bag A, if the chip is blue, the process repeats until a red chip is picked from the bag. When the game is over, the students with the greatest number of Blue Tokens are considered the winning team.

Without any information about the bags, you would probably select a bag simply by guessing. But surprisingly, the show’s producers are going to allow you to do some research before you select a bag. For the next minutes, you can pull a chip from either one of the two bags, look at the chip, and then put the chip back in the bag. You can repeat this process as many times as you want within the minutes. At the end of minutes, you must make your final decision and select which of the bags you want to use in the game.

Getting Started
Assume that the producers of the show do not want give away a lot of their Blue Tokens. As a result, if one bag has the same number of red and blue chips, do you think the other bag would have more, or fewer, blue chips than red chips?
Explain your answer.

Planning the Research
Your teacher will provide you with two bags labeled A and B. You have minutes to experiment with pulling chips one at a time from the bags. After you examine a chip, you must put it back in the bag. Remember, no fair peeking in the bags as that will disqualify you from the game. You can pick chips from just one bag, or you can pick chips from one bag and then the other bag.
Use the results from minutes of research to determine which bag you will choose for the game.

Provide a description outlining how you will carry out your research:
Playing the Game
After the research has been conducted, the competition begins. First, your teacher will shake up Bag A. A chip is selected. If the chip is blue, all students who selected Bag A win an imaginary Blue Token. The chip is put back in the bag, and the process continues. When a red chip is picked from Bag A, students selecting Bag A have completed the competition. Your teacher will now shake up Bag B. A chip is selected. If it is blue, all students who selected Bag B win an imaginary Blue Token. The process continues until a red chip is picked. At that point, the game is over. How many Blue Tokens did you win?

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