Estimating Probabilities by Collecting Data

Examples, videos, and solutions to help Grade 7 students learn how to estimate probabilities by collecting data on an outcome of a chance experiment.

New York State Common Core Math Grade 7, Module 5, Lesson 2

Worksheets for Grade 7

Lesson 2 Student Outcomes

• Students learn how to estimate probabilities by collecting data on an outcome of a chance experiment.
  bull; Students use given data to estimate probabilities.

Lesson 2 Summary

• An estimate for finding the probability of an event occurring is
  
• P(event occurring) = (Number of observed occurrences of the event)/(Total number of observations)

Lesson 2 Classwork
Example 1: Carnival Game
At the school carnival, there is a game in which students spin a large spinner. The spinner has four equal sections numbered 1–4 as shown below. To play the game, a student spins the spinner twice and adds the two numbers that the spinner lands on. If the sum is greater than or equal to , the student wins a prize.

Exercises 1–8
You and your partner will play this game 15 times. Record the outcome of each spin in the table below.

1. Out of the 15 turns how many times was the sum greater than or equal to 5?
2. What sum occurred most often?
3. What sum occurred least often?
4. If students played a lot of games, what proportion of the games played will they win? Explain your answer.
5. Name a sum that would be impossible to get while playing the game.
6. What event is certain to occur while playing the game?
7. Based on your experiment of playing the game, what is your estimate for the probability of getting a sum of 5 or more?
8. Based on your experiment of playing the game, what is your estimate for the probability of getting a sum of exactly 5?

Example 2
A student brought a very large jar of animal crackers to share with students in class. Rather than count and sort all the different types of crackers, the student randomly chose 20 crackers and found the following counts for the different types of animal crackers.
The student can now use that data to find an estimate for the probability of choosing a zebra from the jar by dividing the observed number of zebras by the total number of crackers selected.

Exercises 9–15
If a student were to randomly select a cracker from the large jar:
9. What is your estimate for the probability of selecting a lion?
10. What is the estimate for the probability of selecting a monkey?
11. What is the estimate for the probability of selecting a penguin or a camel?
12. What is the estimate for the probability of selecting a rabbit?
13. Is there the same number of each animal cracker in the large jar? Explain your answer.
14. If the student were to randomly select another 20 animal crackers, would the same results occur? Why or why not?
15. If there are animal crackers in the jar, how many elephants are in the jar? Explain your answer.

Sample Questions
Example 1: Carnival Game
At the school carnival, there is a game in which students spin a large spinner. The spinner has four equal sections numbered 1–4 as shown below. To play the game, a student spins the spinner twice and adds the two numbers that the spinner lands on. If the sum is greater than or equal to , the student wins a prize.

Exercises 1–8
You and your partner will play this game 15 times. Record the outcome of each spin in the table below.

1. What sum occurred most often?
2. What sum occurred least often?
3. Name a sum that would be impossible to get while playing the game.
4. What event is certain to occur while playing the game?
5. Based on your experiment what is the estimate for the probability of getting a sum exactly equal to 5?
6. Out of 15 turns, how many times was the sum greater than or equal to 5?
7. Based on this experiment, what is the estimated probability that the sum would be greater than or equal to 5?
8. If you played this game 300 times, how many times would the sum be greater than or equal to 5?

• Show Step-by-step Solutions

4. A seventh grade student surveyed students at her school. She asked them how many hours a week they spend doing homework. The results are listed in the table below.
   a. Draw a dot plot of the results.
   Suppose a student will be randomly selected.
   b. What is your estimate for the probability of that student spending 7 hours per week doing homework?
   c. What is your estimate for the probability of that student spending more than 7 hours per week doing homework?
   d. If another 25 students were surveyed, do you think they will give the exact same results? Explain your answer.
   e. If there are 600 students at the school, what is your estimate for the number of students who would say they do 5 hours of homework per week?

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A student played a game using one of the spinners below. The table shows the results of spins. Which spinner did the student use? Give a reason for your answer.

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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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