· Web viewNJ Center for Teaching and Learning . . NJ Center for Teaching and Learning . . 7. th. Grade Probability Chapter Questions. How can the collection, organization and

7 th 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?

NJ Center for Teaching and Learning www.njctl.org

Chapter Problems

Introduction to ProbabilityClassworkA 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 marble2) a red marble3) a yellow marble4) a purple marble5) a black marble

HomeworkA 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 77) an even numbered section8) section 1, 2, 3, or 49) section 910) section 8

Experimental and Theoretical ProbabilityClasswork

11) A die is rolled. Complete the table.

Roll Theoretical Probability123456

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

Outcome Number of TimesRoll 1 0Roll 2 3Roll 3 1Roll 4 3Roll 5 2Roll 6 1

Use the above table to find the experimental probability for the following questions.a. rolling a 1


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

HomeworkA 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 ProbabilityABCDE

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

Outcome

Number of Times

A 4B 1C 3D 2E 0

Use the table above to find the experimental probability for the following questions.a. spinning an Ab. spinning a Bc. spinning a Cd. spinning a De. spinning an E

SamplingClasswork

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. Carb. Busc. Subwayd. 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?

Homework21) 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 Artsb. Sciencec. Mathematicsd. 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 ProblemsClasswork

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. Redb. Bluec. Whited. 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?

Homework31) 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 EventsClasswork

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)

Homework41) What is the probability that the first three cards drawn from a full deck of cards are kings?

(without replacement)

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?

Fundamental Counting Principle

Classwork

46) A restaurant has 4 appetizers, 9 entrees, and 5 dessert choices. How many meals are possible? If the restaurant wants to increase their meals as much as possible by adding one more item, should they add an appetizer, an entrée or a dessert?

47) Martha has 8 shirts, 6 pair of pants, and 4 different pair of shoes. Assuming everything matches, how many days can Martha go without wearing the same outfit?

48) How many different 7 digit telephone numbers are there, if the first digit cannot be 0?

49) By adding an area code to each 7 digit telephone number, the phone company increased the amount of telephone numbers by how many? (Remember that the first digit in the area code and the phone number itself cannot be 0.)

50) One state is considering creating license plates where letters cannot be repeated. If the state has license plates consisting of three letters, followed by three different digits, how many fewer license plates are available when repetition of letters is not allowed?


Homework

51) A phone comes in 12 different colors, 5 different head sets, and 7 different styles. How many different phones are available?

52) Mark is taking a 10 question, True/False quiz. How many different ways can the quiz be answered?

53) Frank is calling his sister and can’t remember the first two digits of her phone number. He remembers the remaining five digits. What is the greatest number of attempts that Frank would have to make to complete the call? (He knows that the first digit of his sister’s phone number is not 0.)

54) A combination lock has a combination of 5 single digits, none of which are repeated. How many different combinations are there?

55) A pizza parlor provides customers with the opportunity to create their own single topping pizza by selecting from 4 different crusts, 5 different sauces, 3 different cheeses, and 15 different toppings. How many pizzas are possible? If a second different topping choice is allowed, how many pizzas are possible?

Measures of CenterClassworkUse the stem-and-leaf plot to answer the following questions.

Stem Leaf1 0 0 12 4 5 73 2

Key 1 2 = 12

56) What is the mean?57) What is the median?58) What is the mode?59) Which measure of center best describes the data set? Explain.

HomeworkUse the stem-and-leaf plot to answer the following questions.

Stem Leaf4 5 556 2 2 5 6

Key 1 2 = 1.2


60) What is the mean?61) What is the median?62) What is the mode?63) Which measure of center best describes the data set? Explain.

Measures of VariationClassworkUse the data set to answer the following questions.

6, 6, 8, 2, 3, 2, 5, 0, 1, 2, 3 64) What is the median?65) What is the lower quartile?66) What is the upper quartile?67) What is the least value?68) What is the greatest value?69) What is the interquartile range?70) What is the range?

HomeworkUse the data set to answer the following questions.

12, 21, 15, 12, 27, 22, 19, 19, 20, 2371) What is the median?72) What is the lower quartile?73) What is the upper quartile?74) What is the least value?75) What is the greatest value?76) What is the interquartile range?77) What is the range?

Mean Absolute DeviationClassworkUse 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

xx xx 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 xx x x x

x x x x x xx x x x x x x x

30 31 32 33 34 35 36 37 38 39 40

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

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

80) What is the difference of the means?

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

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

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

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

Points Earned per Game for the Timberwolves

xx

x x xx 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 Giantsx

x x xx x x x xx x x x x x x

0 1 2 3 4 5 6 7 8 9 10

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


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

86) What is the difference of the means?

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

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

89) 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.

47 b.

211

c. 4

d.

423

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.

47

b. 1 c. 0 d.

423

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

a.

58 b.

38 c.

35 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) An ice cream stand has 15 flavors of ice cream, 3 types of syrup, and 10 different toppings. How many different sundaes, consisting of one flavor of ice cream, one syrup, and one topp ing does the s tand serve?

a. 15b. 45

c. 225

d. 450

6) A town has all phone numbers beginning with the same three digits, followed by 4 digits where repetition is allowed. How many different phone numbers are possible?

a. 7,200,000 b. 10,000 c. 720 d. none of these

7) Awards are given to the first, second and third place winners of a race in which 10 people participated. How many possible ways can the awards be given?

a. 6 b. 720 c. 10! d. none of these

8) Ted is choosing 4 songs from an album that contains 18 songs. How many possible arrangements are there for Ted to create if the order of the songs doesn’t matter?


a. 24 b. 3,060 c. 18! d. none of these9) What is the probability of selecting two red cards from a deck of cards? (with replacement)

a.

14 b.

12 c.

34 d. none of these

10) 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

11) The car dealership’s inventory is shown below

Sunrise Car Dealership

Car Make Number of Cars

Ford 550

Nissan 425

BMW 630

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

a. 0.26b. 0.34c. 0.39d. 0.40


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

a.

56 b.

23 c. 1 d. none of these

Short Constructed Response – Write the correct answer for each question. 13) Determine how many three-letter arrangements are possible with the letters

R , A , N , D , O , a n d M if no letter may be repeated.

14) What is the probability of rolling snake eyes on a pair of dice?

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

16) P(rain) = 10% ; P(no rain ) = ___________

17) 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.

18) 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 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) 1/242) 1/43) 1/124) 05) 7/246) 1/87) 1/28) 1/29) 010) 1/811)

Roll

Theoretical Probability

1 1/62 1/63 1/64 1/65 1/66 1/6

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

13)

14)Spin

Theoretical Probability

A ¼B 3/8C 1/8D 1/8E 1/8

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


E

DC B

B

BAA

e. 016) 2,26617) 53918)

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

19) Yes; 9620) 4221) 46122) 132323)

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

24) Yes; 8025) 10826) 37 shots27)

a. 300 Redb. 400 bluec. 200 whited. 100 black

28) 1/6; 1/329) Multiple answers30) ½; 3/5 multiple answers ex: odds will even out31) 100; 532) 1/1000; 60/6000033) 1/100; 10; 10/100034) Multiple answers35) Multiple answers36) 1/3637) 1/12138) 1/2639) 11/85040) 5/1241) 1/552542) 1/443) 1/100044) 1/800045) 1/1546) 180, Appetizer47) 19248) 9,000,00049) 8.1x109

50) 1,422,720


51) 42052) 1,02453) 9054) 30,24055) 900, 96056) 19.8657) 2458) 1059) Mean/median; explanations will vary60) 5.7561) 6.262) 4.5 and 6.263) Median; explanations will vary64) 365) 266) 667) 068) 869) 470) 871) 19.572) 1573) 2274) 1275) 2776) 777) 1578) 33.3679) 36.2580) 2.8981) 1.8982) 2.483) State college84) 6.7585) 3.586) 3.2587) 2.0388) 289) Very similar but timberwolves have a slightly higher variability

Unit Review Answers1) B2) C3) B4) A5) D


6) B7) B8) B9) B10) C11) C12) A13) 120

14)1

36

15)13

20416) 90%

17)4

13



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· Web viewNJ Center for Teaching and Learning . . NJ Center for Teaching and Learning . . 7. th. Grade Probability Chapter Questions. How can the collection, organization and