Engage NY Eureka Math 7th Grade Module 5 Lesson 2 Answer Key

Example 2: Animal Crackers
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. Estimate the probability of selecting a zebra.

The estimated probability of picking a zebra is 3/20, or 0.15 or 15%. This means that an estimate of the proportion of the time a zebra will be selected is 0.15 or 15% of the time. This could be written as P(zebra) = 0.15, or the probability of selecting a zebra is 0.15.

Exercises 1–8: 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 5, the student wins a prize.

Play this game with your partner 15 times. Record the outcome of each spin in the table below.

Exercise 1.
Out of the 15 turns, how many times was the sum greater than or equal to 5?
Answers will vary and should reflect the results from students playing the game 15 times. In the example above, eight outcomes had a sum greater than or equal to 5.

Exercise 2.
What sum occurred most often?
5 occurred the most.

Exercise 3.
What sum occurred least often?
6 and 8 occurred the least. (Anticipate a range of answers, as this was only done 15 times. We anticipate that 2 and 8 will not occur as often.)

Exercise 4.
If students were to play a lot of games, what fraction of the games would they win? Explain your answer.
Based on the above outcomes, $$\frac{8}{15}$$ represents the fraction of outcomes with a sum of 5 or more. To determine this, count how many games have a sum of 5 or more. There are 8 games out of the total 15 that have a sum of 5 or more.

Exercise 5.
Name a sum that would be impossible to get while playing the game.
Answers will vary. One possibility is getting a sum of 100. Any sum less than 2 or greater than 8 would be correct.

Exercise 6.
What event is certain to occur while playing the game?
Answers will vary. One possibility is getting a sum between 2 and 8 because all possible sums are between 2 and 8, inclusive.

When you were spinning the spinner and recording the outcomes, you were performing a chance experiment. You can use the results from a chance experiment to estimate the probability of an event. In Exercise 1, you spun the spinner 15 times and counted how many times the sum was greater than or equal to 5. An estimate for the probability of a sum greater than or equal to 5 is
P(sum ≥5) = $$\frac{\text { Number of observed occurrences of the event }}{\text { Total number of observations }}$$
Exercise 7.
Based on your experiment of playing the game, what is your estimate for the probability of getting a sum of 5 or more?
Answers will vary. Students should answer this question based on their results. For the results indicated above, $$\frac{8}{15}$$ or approximately 0.53 or 53% would estimate the probability of getting a sum of 5 or more.

Exercise 8.
Based on your experiment of playing the game, what is your estimate for the probability of getting a sum of exactly 5?
Answers will vary. Students should answer this question based on their results. Using the above 15 outcomes, $$\frac{4}{15}$$ or approximately 0.27 or 27% of the time represents an estimate for the probability of getting a sum of exactly 5.

Exercises 9–15
If a student randomly selected a cracker from a large jar:
Exercise 9.
What is your estimate for the probability of selecting a lion?
$$\frac{2}{20}$$ = $$\frac{1}{10}$$ = 0.1

Exercise 10.
What is your estimate for the probability of selecting a monkey?
$$\frac{4}{20}$$ = $$\frac{1}{5}$$ = 0.2

Exercise 11.
What is your estimate for the probability of selecting a penguin or a camel?
$$\frac{(3+1)}{20}$$ = $$\frac{4}{20}$$ = $$\frac{1}{5}$$ = 0.2

Exercise 12.
What is your estimate for the probability of selecting a rabbit?
$$\frac{0}{20}$$ = 0

Exercise 13.
Is there the same number of each kind of animal cracker in the jar? Explain your answer.
No. There appears to be more elephants than other types of crackers.

Exercise 14.
If the student randomly selected another 20 animal crackers, would the same results occur? Why or why not?
Probably not. Results may be similar, but it is very unlikely they would be exactly the same.

Exercise 15.
If there are 500 animal crackers in the jar, how many elephants are in the jar? Explain your answer.
$$\frac{5}{20}$$ = $$\frac{1}{4}$$ = 0 .25; hence, an estimate for the number of elephants would be 125 because 25% of 500 is 125.

Eureka Math Grade 7 Module 5 Lesson 2 Problem Set Answer Key

Question 1.
Play a game using the two spinners below. Spin each spinner once, and then multiply the outcomes together. If the result is less than or equal to 8, you win the game. Play the game 15 times, and record your results in the table below. Then, answer the questions that follow.

a. What is your estimate for the probability of getting a product of 8 or less?
b. What is your estimate for the probability of getting a product of more than 8?
c. What is your estimate for the probability of getting a product of exactly 8?
d. What is the most likely product for this game?
e. If you play this game another 15 times, will you get the exact same results? Explain.

a. Answers should be approximately 7, 8, or 9 divided by 15. The probability for the sample spins provided is $$\frac{9}{15}$$, or $$\frac{3}{5}$$.

b. Subtract the answer to part (a) from 1, or 1- the answer from part (a). Approximately 8, 7, or 6 divided by 15. The probability for the sample spins provided is $$\frac{6}{15}$$, or $$\frac{2}{5}$$.

c. Approximately 1 or 2 divided by 15. The probability for the sample spins provided is $$\frac{1}{15}$$.

d. Possibilities are 4, 6, 8, and 12. The most likely product in the sample spins provided is 4.

e. No. Since this is a chance experiment, results could change for each time the game is played.

Question 2.
A seventh-grade student surveyed students at her school. She asked them to name their favorite pets. Below is a bar graph showing the results of the survey.

Use the results from the survey to answer the following questions.
a. How many students answered the survey question?
b. How many students said that a snake was their favorite pet?

Now, suppose a student is randomly selected and asked what his favorite pet is.
c. What is your estimate for the probability of that student saying that a dog is his favorite pet?
d. What is your estimate for the probability of that student saying that a gerbil is his favorite pet?
e. What is your estimate for the probability of that student saying that a frog is his favorite pet?
a. 31
b. 5
c. (Allow any form.) $$\frac{9}{31}$$, or approximately 0.29 or approximately 29%
d. (Allow any form.) $$\frac{2}{31}$$, or approximately 0.06 or approximately 6%
e. $$\frac{0}{31}$$, or 0 or 0%

Question 3.
A seventh-grade student surveyed 25 students at her school. She asked them how many hours a week they spend playing a sport or game outdoors. 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 answering 3 hours?
c. What is your estimate for the probability of that student answering 8 hours?
d. What is your estimate for the probability of that student answering 6 or more hours?
e. What is your estimate for the probability of that student answering 3 or fewer hours?
f. If another 25 students were surveyed, do you think they would give the exact same results? Explain your answer.
g. If there are 200 students at the school, what is your estimate for the number of students who would say they play a sport or game outdoors 3 hours per week? Explain your answer.
a.
b. $$\frac{7}{25}$$ = 0.28 = 28%
c. $$\frac{1}{25}$$ = 0.04 = 4%
d. $$\frac{3}{25}$$ = 0.12 = 12%
e. $$\frac{19}{25}$$ = 0.76 = 76%
f. No. Each group of 25 students could answer the question differently.

g. 200 ∙ ($$\frac{7}{25}$$) = 56
I would estimate that 56 students would say they play a sport or game outdoors 3 hours per week. This is based on estimating that, of the 200 students, $$\frac{7}{25}$$ would play a sport or game outdoors 3 hours per week, as $$\frac{7}{25}$$ represented the probability of playing a sport or game outdoors 3 hours per week from the seventh-grade class surveyed.

Question 4.
A student played a game using one of the spinners below. The table shows the results of 15 spins. Which spinner did the student use? Give a reason for your answer.

Spinner B. Tallying the results: 1 occurred 6 times, 2 occurred 6 times, and 3 occurred 3 times. In Spinner B, the sections labeled 1 and 2 are equal and larger than section 3.

Eureka Math Grade 7 Module 5 Lesson 2 Exit Ticket Answer Key

In the following problems, round all of your decimal answers to three decimal places. Round all of your percents to the nearest tenth of a percent.
A student randomly selected crayons from a large bag of crayons. The table below shows the number of each color crayon in a bag. Now, suppose the student were to randomly select one crayon from the bag.

Question 1.
What is the estimate for the probability of selecting a blue crayon from the bag? Express your answer as a fraction, decimal, or percent.
$$\frac{5}{30}$$ = $$\frac{1}{6}$$ ≈ 0.167 or 16.7%

Question 2.
What is the estimate for the probability of selecting a brown crayon from the bag?
$$\frac{10}{30}$$ = $$\frac{1}{3}$$ ≈ 0.333 or 33.3%

Question 3.
What is the estimate for the probability of selecting a red crayon or a yellow crayon from the bag?
$$\frac{9}{30}$$ = $$\frac{3}{10}$$ = 0.3 = 30%

Question 4.
What is the estimate for the probability of selecting a pink crayon from the bag?
$$\frac{0}{30}$$ = 0%
There are 6 out of 30, or $$\frac{1}{5}$$ or 0.2, crayons that are red. Anticipate $$\frac{1}{5}$$ of 300 crayons are red, or approximately 60 crayons.