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 can the understanding and use of measures of central tendency be useful for interpreting and drawing conclusions about data?

3. How can devising and carrying out surveys and simulations help to determine the possible outcomes and probability of simple events?

4. How can the formulation of questions and conjectures be prompted by the analysis of data?

5.How can data be organized so that inferences and predictions can be developed and evaluated?

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

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

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

#12 – 16 List the experimental probability for rolling a:

Roll / Experimental Probability
1
2
3
4
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 D, and one section has the letter E.

  1. Draw a picture of the spinner

18. Use your drawing to fill in the chart

Spin / Theoretical Probability
A
B
C
D
E

The spinner is spun 10 times and the outcomes are:

Outcome / Number of Times
A / 4
B / 1
C / 3
D / 2
E / 0

#19 – 22 List the experimental probability for spinning a:

Spin / Experimental Probability
A
B
C
E

Word Problems

Classwork

23. 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.

  1. 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:

Red

Blue

White

Black

  1. 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?

  1. Create a situation where the experimental probability and the theoreticalprobability have the same value.
  1. A coin is flipped. What is thetheoretical probability for flipping a tail? Mark and John flip a coin twenty times and get 8heads, 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

  1. 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.
  1. 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?
  1. 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 a case?
  1. Create a situation where the experimental probability is greater than the theoretical probability.
  1. How does understanding probability help someone who plays cards?

Fundamental Counting Principle

Classwork

  1. 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?
  1. 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?
  1. How many different 7 digit telephone numbers are there, if the first digit cannot be 0?
  1. 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.)
  1. 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

  1. A phone comes in 12 different colors, 5 different head sets, and 7 different styles. How many different phones are available?
  1. Mark is taking a 10 question, True/False quiz. How many different ways can the quiz be answered?
  1. 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.)
  1. A combination lock has a combination of 5 single digits, none of which are repeated. How many different combinations are there?
  1. 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?

Permutations and Combinations

Classwork

43. What is the value of the following:

a. 6P2

b. 8P3

c. 10P2

d.3P3

44. 30 dogs and their handlers enter a show ring. The judge will pick 5 dogs to place in the contest. How many different ways can the first, second, third, fourth, and fifth place be awarded?

45a. You create a sundae with 3 out of 10 flavors at the Ice Cream Store. This is an example of______.

b. You must fit 10 out of 15 dogs in the cages along the wall (one dog per cage). How many different ways are there to place them in the cages? This is an example of ______.

46. Find the value of the following:

a. 6C4

b. 5C1

c. 4C4

d. 6C2

47. There are 21 girls on a soccer team. Four of these girls will be picked to be on the All-American Team. How many different groups of players can be chosen?

Homework

48. What is the value of the following:

a. 10P6

b. 9P4

c. 5P5

d. 4P1

49. 20 snowboarders enter a race. The top 4 will get medals. How many different ways can the first, second, third, and fourth medals be given?

50a. You must buy 3 kinds of soda out of 8 at the store. This is an example of ______.

b. Your parents inform you that you can only invite 30 people out of the 50 people that you wanted to invite to your party. The possibilities of the people you can invite is an example of ______.

51. Find the value of the following:

a. 10C8

b. 4C2

c. 6C5

d. 3C3

52. There are 20 children in a kindergarten class. Five of these children will be picked for the outstanding kindergarten award. How many different groups of kindergarteners can be chosen?

Probability of Compound Events

Classwork

53.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?

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

55. 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)

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

57. 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

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

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

60. 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?

61. 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?

62. 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?

Probabilities of Mutually Exclusive and Overlapping Events

Classwork

63. Are these events mutually exclusive?

Event A: Roll an even number

Event B: Roll a prime number

64. Are these events mutually exclusive?

Event A: Select a bird

Event B: Select a bald eagle

Calculate:

65. P(selecting a queen or a 10) from a deck of cards

66. P(rolling a 2 or a 6) on a die

67. P(rolling a 2 or an even number) on a die

Homework

68. Are these events mutually exclusive?

Event A: Roll a number greater than 2

Event B: Roll a number less than 3

69. Are these events mutually exclusive?

Event A: Select a consonant from the alphabet

Event B: Select a vowel from the alphabet

Calculate:

70. P(choosing a 4 or a jack) from a deck of cards

71. P(rolling an odd number or a number greater than 3) on a die

72. P(choosing a club or a black card) from a deck of cards

Complementary Events

Classwork

73. P(snow) = 20%

P(no snow) =

74. P(A) = .9

P(not A) =

75. What is the probability of not selecting a queen from a deck of cards?

76. What is the probability of not rolling a 1 on a die?

77. What is the probability of not selecting a queen or a king from a full deck of cards?

Homework

78. P(rain) = 5%

P(no rain) =

79. P(A) = 3/5

P(not A) =

80. What is the probability of not selecting a four from a deck of cards?

81. What is the probability of not rolling a 6 on a die?

82. If 22% of the people in the room are bald, what percent are not bald?

Unit Review

Multiple Choice– Choose the correct answer for each question.

  1. A bag contains 8 red marbles, 3 green marbles, 2 white marbles and 1 yellow marble. What is the probability of selecting a red marble?

a. b. c. 8 d.

  1. The theoretical probability for selecting a heart from a deck of cards is _____

a. b. c. d.

  1. A die is rolled 5 times and a “2” is rolled each time. What is the experimental probabilityfor rolling a 5?

a. b. c. 0 d. 1

4. Patty selects 5 winning tickets out of a bucket containing 100 tickets. Use experimental probability to predict the number of winning tickets in a drum that contains 1800 tickets.

a. 900 b. 180 c. 100 d. 90

  1. Mark bowls a strike 25% of the time. If he rolls the bowling ball 80 times, how many strikes should he expect to make?

a. 25 b. 20 c. 10 d. 8

  1. A delihasfourtypesofmeat,threetypesofcheese,andtwotypesof bread.Howmanydifferentsandwiches,consistingofonetypeofmeat, onetypeof cheese,andonetypeof bread,doesthedeliserve?

(a)9(c) 30

(b)24(d) 75

  1. License plates contain 3 digits, followed by 3 letters.If repetition is allowed,how many different plates are possible?

a. 17,576,000 b. 11,232,000 c. 102 d. none of these

  1. Awards are given to the first and second place winners in a race in which 1,000 people participated. How many possible ways can the awards be given?

a. 1,099 b. 999,000 c. 3! d. none of these

  1. Bill is choosing 3 toppings from a list of 20 for his sundae. How many possible sundaesare there for Bill to create?

a. 6840 b. 1140 c. 5! d. none of these

10. What is the probability of selecting two red cards from a deck of cards? (with replacement)

a. b. c. d.

11. A program generates 2 numbers from 1 to 5. What is the probability that the same number will occurboth times?

a. b. c. d. none of these

  1. The party registrationofthevoters inJonesvilleisshowninthetable below

RegisteredVotersin
Jonesville
PartyRegistration / NumberofVoters
Registered
Democrat / 6,000
Republican / 5,300
Independent / 3,700

IfoneoftheregisteredJonesvillevotersisselected atrandom, whatis theprobabilitythattheperson selectedisaRepublican?

(a) 0.353(c) 0.600

(b) 0.400(d) 0.667

  1. What is the probability of rolling a prime number on a die?

a. b. c. 1 d. none of these

Short Constructed Response – Write the correct answer for each question.

  1. Determinehowmany four-letterarrangementsarepossiblewiththeletters in the word NUMBER if nolettermay berepeated.
  1. What is the probability of rolling a snake eyes on a pair of dice?
  2. P(winning) = 22% ; P(losing) = ______
  3. What is the probability of selecting a club or a three from a deck of cards?

Extended Constructed Response – Solve the problem, showing all work. Partial credit may be given.

  1. You and a friend are at the game section of a carnival. There is a big die that is rolled 12 times. For four of the rolls, the die landed on the number “6”; the die landed on a different number for each of the other eight rolls. Use this information to answer the following questions:
  2. What is the theoretical probability for rolling a “6”?
  3. What is the experimental probability for rolling a “6”?
  4. Use experimental probability to determine the number of times the die would be expected to land on a “6” if it is rolled 60 times.
  5. If you were to roll the die, would you be more likely to roll a “6”? Why or why not?

NJ Center for Teaching and Learning

Answer Key Probability

  1. 1/24
  2. ¼
  3. 1/12
  4. 0
  5. 0
  6. 1/8
  7. ½
  8. ½
  9. 0
  10. 1/8

Roll / Theoretical Probability
1 / 1/6
2 / 1/6
3 / 1/6
4 / 1/6
5 / 1/6
6 / 1/6
  1. 0/10
  2. 3/10
  3. 1/10
  4. 3/10
  5. 2/10

Spin / Theoretical Probability
A / ¼
B / ½
C / 1/8
D / 1/8
E / 1/8
  1. 4/10
  2. 1/10
  3. 3/10
  4. 0/10
  5. 37 shots
  6. 300 Red, 400 Blue, 200 White, 100 Black
  7. 1/6, 1/3
  8. Multiple Answers
  9. ½, 12/20, Multiple Answers ex: odds will even out
  10. 100, 5
  11. 1/1000, 60/60000
  12. 1/100, 10, 10/1000
  13. Multiple Answers
  14. Multiple Answers
  15. 180, Appetizer
  16. 192
  17. 9000000
  18. 8.1 x 109
  19. 6344000
  20. 420
  21. 1024
  22. 90
  23. 30240
  24. 900, 960
  25. 30
  26. 336
  27. 6
  28. 17100720
  29. Combination
  30. Permutation
  31. 15
  32. 5
  33. 1
  34. 15
  35. 5985
  36. 151200
  37. 3024
  38. 120
  39. 4
  40. 116280
  41. Combination
  42. Combination
  43. 45
  44. 6
  45. 6
  46. 1
  47. 15504
  48. 1/36
  49. 1/121
  50. 1/26
  51. 11/4165
  52. 5/12
  53. 1/5525
  54. ¼
  55. 1/1000
  56. 1/8000
  57. 1/15
  58. No
  59. No
  60. 8/52
  61. 2/6
  62. 3/6
  63. Yes
  64. Yes
  65. 8/52
  66. 5/6
  67. ½
  68. 80%
  69. .1
  70. 48/52
  71. 5/6
  72. 44/52
  73. .5
  74. 2/5
  75. 48/52
  76. 5/6
  77. 88%

NJ Center for Teaching and Learning

Review Answers

  1. A
  2. B
  3. C
  4. D
  5. B
  6. B
  7. A
  8. B
  9. B
  10. D
  11. C
  12. A
  13. A
  14. 360
  15. 1/36
  16. 78%
  17. 4/13
  18. A. 1/6

B. 1/3

C. 20

D. No

NJ Center for Teaching and Learning