# Probability

## Objective

Conduct simulations with multiple events to determine probabilities.

## Common Core Standards

### Core Standards

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• 7.SP.C.8 — Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

• 7.SP.C.8.C — Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

## Criteria for Success

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1. Conduct a simulation for a situation involving more than one event (compound event).
2. Analyze the results from a simulation of a compound event to estimate the probability of the compound event.
3. Use experiments or simulations to analyze and critique the reasoning of others (MP.3).

## Tips for Teachers

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• The following materials are needed for this lesson: coins, dice, counters, The Horse Race board (found on page S-3 of Analyzing Games of Chance), and the Race Results Sheet (found on page S-5 of Analyzing Games of Chance). See the notes for each Anchor Problem for more details.
• In this lesson, students are introduced to compound events through experiments and simulations. They are able to see experimentally how the sample space for compound events is different from the sample space for simple events. In the next lesson, students will learn how to organize their sample space for compound events using lists, tables, or tree diagrams.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

Steve is a basketball player on your school’s team. During a game, he gets to take two shots from the free-throw line. On average, Steve makes a shot from the free-throw line half of the time. What is the probability that he will make both shots?

Al says: “The three possible results are that Steve makes $0$ shots, $1$ shot, or $2$ shots. So, each result has a probability of ${1\over3}$.”

Use a coin or a number cube to simulate multiple trials of this situation. Then analyze your results and determine if Al’s statement is accurate or not.

#### References

SERP Poster Problems Try, Try AgainHandout #1

Try, Try Again from Poster Problems is made available by SERP under the CC BY-NC-SA 4.0 license. Accessed April 5, 2018, 1:28 p.m..

Modified by The Match Foundation, Inc.

### Problem 2

Eleven horses enter a race. The first one to pass the finish line wins.

Using The Horse Race board, place counters on the starting squares labeled 2 to 12. Share out the horses so that each person in your group has three or four horses.

How to play:

• Roll the two dice and add the scores.
• The horse with that number moves one square forward.
• Keep rolling the dice.
• The horse that is first past the finish line wins.
1. Before you start the race, write down the order you predict the horses will finish in on the Race Results sheet. Why did you predict this? Write down your reason next to your prediction in the space provided.
2. Play the game twice. Record the final positions of the horses each time.
3. Try to explain any patterns you find in your data.
1. Does the outcome vary very much from race to race?
2. Which horses are most likely to win? Why?
3. Which horses are least likely to win? Why?
4. Could the finishing order have been predicted?
5. Could the winning horse have been predicted?

#### References

MARS Formative Assessment Lessons for Grade 7 Analyzing Games of ChanceThe Horse Race

Analyzing Games of Chance from the Classroom Challenges by the MARS Shell Center team at the University of Nottingham is made available by the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed April 5, 2018, 1:29 p.m..

Modified by The Match Foundation, Inc.

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

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Aimee has two sisters in her family. She thinks the probability of a family having three children who are all girls is ${{{{1\over4}}}}$ because there can be 0 girls, 1 girl, 2 girls, or 3 girls.

Aimee designs a simulation to test her prediction. She flips a coin three times in a row and records the results. She uses heads to represent a girl and tails to represent a boy. After 10 trials of this simulation, Aimee gets the following results.

 Trial 1 2 3 4 5 6 7 8 9 10 Results BBB GBB GGG GGB BBG GGB BGG BGB BBG GBB
1. Does ${{{{1\over4}}}}$ seem like a reasonable probability of having 3 girls? Explain your reasoning.
2. Estimate the probability of having 3 girls using the results from Aimee’s simulation.

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