7th Grade Probability Chapter Questions - NJCTLcontent.njctl.org/courses/math/7th-grade/...NJ Center for Teaching and Learning ~ 8 ~ Mean Absolute Deviation Classwork Use the following

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7th Grade Probability Chapter Questions

1. How can the collection, organization and display of data help to interpret, evaluate inferences and make predictions about real-life situations and circumstances?

2. How does probability relate to real world application problems?

3. How can measures of center and variation be used to compare two sets of data?

4. How are different events classified and what can I use to solve them?

5. How can finding the ways to count the possible outcomes of compound events be used to determine their probability?


Chapter Problems Introduction to Probability Classwork A jar contains 6 red, 8 blue, one white, 7 black, and two yellow marbles. Use this information to determine the probability of selecting:

1) a white marble 2) a red marble 3) a yellow marble 4) a purple marble 5) a black marble

Homework A spinner is divided into 8 sections of equal size. The sections are numbered 1 through 8. Use this information to determine the probability of the needle landing on:

6) section 7 7) an even numbered section 8) section 1, 2, 3, or 4 9) section 9 10) section 8

Experimental and Theoretical Probability Classwork

11) A die is rolled. Complete the table.

Roll Theoretical Probability

1

2

3

4

5

6


12) A die is rolled 10 times and the outcomes are:

Outcome Number of Times

Roll 1 0

Roll 2 3

Roll 3 1

Roll 4 3

Roll 5 2

Roll 6 1

Use the above table to find the experimental probability for the following questions.

a. rolling a 1 b. rolling a 2 c. rolling a 3 d. rolling a 4 e. rolling a 5

Homework A spinner contains 8 equally divided sections, two sections have the letter A, 3 sections have the letter B, one section has the letter C, one section has the letter D, and one section has the letter E.

13) Draw a picture of the spinner. 14) Use your drawing to fill in the chart.

Spin Theoretical Probability

A

B

C

D

E

15) The spinner is spun 10 times and the outcomes are:

Outcome Number of Times

A 4

B 1

C 3

D 2

E 0

Use the table above to find the experimental probability for the following questions.

a. spinning an A b. spinning a B c. spinning a C d. spinning a D e. spinning an E


Sampling Classwork

16) In a survey of 300 voters, 68 said they voted for Candidate A. How many votes can Candidate A expect to receive if the population of the town is 10,000?

17) In a capture-recapture study, 97 grizzly bears were tagged and released back into the wild. A

month later, 200 bears were captured of which 36 were tagged. About how many grizzly bears are in the population?

18) From a survey of 100 commuters about how they get to work, 38 said they drive their cars, 47

said they take the bus, 14 said they take the subway, and 1 said they ride their bicycle. Out of 4,800 commuters, predict how many will commute to work in each of the following way.

a. Car b. Bus c. Subway d. Bicycle

19) To determine the consistency of a printer, 100 printed sheets are randomly checked and 4

sheets are defective. Is this sample reliable? About how many defective sheets would be expected if 2,400 sheets were printed?

20) The cafeteria employees would like to start selling fruit in the morning. They surveyed 24 students by asking every 8th student that entered the cafeteria for breakfast. Four students said they preferred apples, 3 preferred oranges, and 1 preferred peaches. If 336 students purchase breakfast daily, about how many students can they expect to pick an orange?

Homework

21) In a capture-recapture study, 83 mountain lions were tagged and released back into the wild. Several months later, 300 mountain lions were captured, of which 54 were tagged. About how many mountain lions are in the population?

22) In a survey of 1056 voters at Roberts School, 274 said they voted for Candidate A. How many votes can Candidate A expect to receive if there were 5,101 votes?

23) From a survey of 80 students about their favorite subjects, 24 said Language Arts, 16 said Science, 31 said Mathematics, and 9 said Social Studies. Out of 960 students, predict how many will favor each subject.

a. Language Arts b. Science c. Mathematics d. Social Studies

24) A DVD player manufacturing company wants to test the quality of their DVD players. They randomly pick 50 DVD players to test and determine that 4 are defective. Is this sample reliable? About how many defective DVD players would you expect if 1,000 DVD players are made?


25) A library wants to expand their children’s book section. The librarians surveyed 30 children by asking every 6th child that visited the library to figure out what genres were most popular. The children’s responses were: 12 liked fiction, 8 liked non-fiction, 4 liked science fiction, and 6 liked mystery. If the library expects 540 children to visit the library in a week, about how many children will check out a mystery book?

Word Problems Classwork

26) You made 8 out of 15 shots on goal. Use experimental probability to predict how many goals you will make tomorrow if you take 70 shots.

27) There are 1000 buttons in the jar. You randomly select 10 buttons and get 3 red, 4 blue, 2 white, 1 black. Use experimental probability to predict how many buttons in the jar are:

a. Red b. Blue c. White d. Black

28) A die is rolled. What is the theoretical probability for rolling a 3? Mary rolls a die six times and rolls a 3, on two of the rolls. What is the experimental probability for rolling a 3?

29) Create a situation where the experimental probability and the theoretical probability have the same value.

30) A coin is flipped. What is the theoretical probability for flipping a tail? Mark and John flip a coin twenty times and get 8 heads, 12 tails. What is the experimental probability for flipping a tail? If Mark & John flip the coin 100 times, what do you think will happen to the experimental probability?

Homework

31) Bart makes 20% of his free throws. If he takes 500 free throws, how many go in the basket? Predict how many baskets Bart makes when he takes 25 free throws.

32) A factory produces 1000 light bulbs per minute. Each minute, one bulb produced will be defective. What is the theoretical probability of selecting the defective bulb from the light bulbs produced in one minute? What is the theoretical probability of selecting a defective bulb from the light bulbs produced in one hour?

33) Every 100th box of candy contains a prize. What is the theoretical probability for selecting the box of candy with a prize? A case contains 1000 boxes and how many prizes? What is the probability of selecting a box containing a prize from a case?

34) Create a situation where the experimental probability is greater than the theoretical probability.

35) How does understanding probability help someone who plays cards?


Probability of Compound Events Classwork

36) You are given a pair of dice. One die is numbered 1 through 6 but the other die is numbered 7 through 12. What are the odds of rolling a 3 and an 8?

37) A machine generates numbers randomly from balls numbered 5 through 15. Two numbers are selected, with replacement. What are the odds that both the numbers picked will be 8?

38) A bag with 6 blue marbles, 3 green marbles, and 4 orange marbles is lying on a table. What is the probability that John will pick 2 green marbles? (without replacement)

39) What is the probability that the first three cards drawn from a full deck of cards are clubs? (without replacement)

40) There are 6 male puppies and 3 female puppies. What is the probability that the first two puppies chosen will be males? (without replacement)

Homework

41) What is the probability that the first three cards drawn from a full deck of cards are kings?

42) You dropped two coins. What is the probability that they will both land on heads?

43) Bill Gates wrote a computer program that generates three random numbers between 1 and 10. What is the probability that all three values will be three?

44) A lottery machine generates numbers randomly. Three numbers are picked between 1 and 20. What is the probability that all three numbers that are picked are 17?

45) There are 4 blue marbles and 2 red marbles. A marble is selected and not returned. What is the probability that two red marbles will be chosen?

Measures of Center Classwork Use the stem-and-leaf plot to answer the following questions.

Stem Leaf

1 0 0 1

2 4 5 7

3 2

Key 1 2 = 12

46) What is the mean? 47) What is the median? 48) What is the mode? 49) Which measure of center best describes the data set? Explain.


Homework Use the stem-and-leaf plot to answer the following questions.

Stem Leaf

4 5 5

5

6 2 2 5 6

Key 1 2 = 1.2

50) What is the mean? 51) What is the median? 52) What is the mode? 53) Which measure of center best describes the data set? Explain.

Measures of Variation Classwork Use the data set to answer the following questions.

6, 6, 8, 2, 3, 2, 5, 0, 1, 2, 3 54) What is the median? 55) What is the lower quartile? 56) What is the upper quartile? 57) What is the least value? 58) What is the greatest value? 59) What is the interquartile range? 60) What is the range?

Homework Use the data set to answer the following questions.

12, 21, 15, 12, 27, 22, 19, 19, 20, 23 61) What is the median? 62) What is the lower quartile? 63) What is the upper quartile? 64) What is the least value? 65) What is the greatest value? 66) What is the interquartile range? 67) What is the range?


Mean Absolute Deviation Classwork Use the following data to answer the next set of questions. Round your answers to the nearest hundredth.

Number of Students per Class at the Local Community College x x x x x x x x x x x x x x 30 31 32 33 34 35 36 37 38 39 40

Number of Students per Class at the State College x x x x x x x x x x x x x x x x x x x x 30 31 32 33 34 35 36 37 38 39 40

68) What is the mean number of students per class at the local community college?

69) What is the mean number of students per class at the state college?

70) What is the difference of the means?

71) What is the mean absolute deviation of the data set for the local community college?

72) What is the mean absolute deviation of the data set for the state college?

73) Which college has more variability in the number of students it has per class? Explain your answer.


Homework Use the following data to answer the next set of questions. Round your answers to the nearest hundredth.

Points Earned per Game for the Timberwolves x x x x x x x x x x x x x x x x 0 1 2 3 4 5 6 7 8 9 10

Points Earned per Game for the Little Giants x x x x x x x x x x x x x x x x 0 1 2 3 4 5 6 7 8 9 10

74) What is the mean number of points earned by the Timberwolves per game?

75) What is the mean number of points earned by the Little Giants per game?

76) What is the difference of the means?

77) What is the mean absolute deviation of the data set for the Timberwolves?

78) What is the mean absolute deviation of the data set for the Little Giants?

79) Which team has more variability in the number of points it earns per game? Explain your answer.


Probability Unit Review Multiple Choice – Choose the correct answer for each question. 1) A bag contains 12 red marbles, 4 black marbles, 4 purple marbles and 2 pink marbles. What

is the probability of selecting a black marble?

a. 7

4 b.

11

2

c. 4 d.

23

4

2) A bag contains 12 red marbles, 4 black marbles, 4 purple marbles and 2 pink marbles. What

is the probability of selecting a white marble?

a. 7

4

b. 1 c. 0 d.

23

4

3) A die is rolled 8 times and a “5” is rolled three times. What is the experimental probability for

rolling a 5?

a. 8

5 b.

8

3 c.

5

3

d. 1

4) Sam hits the baseball 15% of the time. If he swings the bat 40 times, how many hits should

he expect to make?

a. 6 b. 15 c. 20 d. 40 5) What is the probability of selecting two red cards from a deck of cards? (with replacement)

a. 4

1 b.

2

1 c.

4

3 d. none of these

6) In a sample of 75 randomly selected students at a school, 32 are female. There are

1,371 students in the school. Using these results, predict the number of females in

the school.

a. 275

b. 343

c. 585

d. 686


7) The car dealership’s inventory is shown below

If a car is selected at random, what is the probability that the car selected is not a Ford or Nissan?

a. 0.26 b. 0.34 c. 0.39 d. 0.4

8) What is the probability of rolling a prime number or a number greater than 3 on a die?

a.6

5 b.

3

2 c. 1 d. none of these

Sunrise Car Dealership

Car Make Number of Cars

Ford 550

Nissan 425

BMW 630


Short Constructed Response – Write the correct answer for each question. 8) What is the probability of rolling snake eyes on a pair of dice?

9) What is the probability of selecting a club and a heart from a deck of cards (without replacement)?

10) P(rain) = 10% ; P(no rain ) = ___________ 11) What is the probability of selecting a club or a jack from a deck of cards?


Extended Constructed Response – Solve the problem, showing all work. 12) The amount of December snowfall, in inches, was recorded on the dot plots below. Use the

following dot plots to answer the questions below.

Snowfall – Oswego, NY x x x x x x x x x x x x x x x x x x x x x x x x x x 18 19 20 21 22 23 24 25 26 27 28

Snowfall – Fulton, NY

x x x x x x x x x x x x x x x x

24 25 26 27 28 29 30 31 32 33 34 a. What is the mean amount of snowfall in each town?

b. What is the difference of the two means?

c. What is the mean absolute deviation of each of the data sets?

d. Which town has more variability in the amount of December snowfall?


Answer Key

1) 1/24 2) 1/4 3) 1/12 4) 0 5) 7/24 6) 1/8 7) 1/2 8) 1/2 9) 0 10) 1/8 11)

Roll Theoretical Probability

1 1/6

2 1/6

3 1/6

4 1/6

5 1/6

6 1/6

12) a. 0 b. 3/10 c. 1/10 d. 3/10 e. 1/5

13)

14)

Spin Theoretical Probability

A ¼

B ½

C 1/8

D 1/8

E 1/8

15) a. 2/5 b. 1/10 c. 3/10 d. 1/5 e. 0

16) 2,266

17) 539 18)

a. 1,824 b. 2,256 c. 672 d. 48

19) Yes; 96 20) 42 21) 461 22) 1323 23)

a. 288 b. 192 c. 372 d. 108

24) Yes; 80 25) 108 26) 37 shots 27)

a. 300 Red b. 400 blue c. 200 white d. 100 black

28) 1/6; 1/3 29) Multiple answers 30) ½; 3/5 multiple answers ex: odds will

even out 31) 100; 5 32) 1/1000; 60/60000 33) 1/100; 10; 10/1000 34) Multiple answers 35) Multiple answers 36) 1/36 37) 1/121 38) 1/26 39) 11/850 40) 5/12 41) 1/5525 42) 1/4 43) 1/1000 44) 1/8000 45) 1/15 46) 19.86 47) 24 48) 10 49) Mean/median; explanations will vary 50) 5.75 51) 6.2

A A B

B

B C

D

E


52) 4.5 and 6.2 53) Median; explanations will vary 54) 3 55) 2 56) 6 57) 0 58) 8 59) 4 60) 8 61) 19.5 62) 15 63) 22 64) 12 65) 27 66) 7 67) 15 68) 33.36 69) 36.25 70) 2.89 71) 1.89 72) 2.3 73) State college 74) 1.53 75) 1.26 76) 6.75 77) 3.5 78) 3.25 79) 2.03 80) 2 81) Very similar but Timberwolves have a

slightly higher variability 82) 1.6 83) 1.625

Unit Review Answers

1) B

2) C

3) B

4) A

5) B

6) C

7) C

8) 120

9) 1

36

10) 13

204

11) 90%

12) 1

2

13) Oswego: 24.2”

Fulton: 28.1”

Difference: 3.9”

Absolute Deviation:

-Oswego: 2.3”

-Fulton: 2.25

Variability is about the same, Oswago is

slightly higher

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7th Grade Probability Chapter Questions - NJCTLcontent.njctl.org/courses/math/7th-grade/...NJ Center for Teaching and Learning ~ 8 ~ Mean Absolute Deviation Classwork Use the following