new probability probability of simple events: classwork 1. p 2. p...

Geometry – Probability ~1~ NJCTL.org

Probability

Probability of Simple Events: CLASSWORK

You are rolling a standard number cube. Find the theoretical probability of each outcome.

1. P(rolling a 5) 2. P(rolling a 6)

3. P(rolling an even number) 4. P(rolling a 1)

5. P(rolling a multiple of 3) A bag contains 2 red ping-pong balls, 3 green ping-pong balls, 3 blue ping-pong balls, and 1 yellow ping-pong ball. Find the probability of randomly selecting each outcome.

6. P(green) 7. P(not red)

8. P(red or blue) 9. P(red)

Two standard number cubes are rolled. Find each probability. 10. P(a sum equal to 2) 11. P(sum not equal to 2) 12. P(a product less than or equal to 2) 13. P(a sum equal to 12)


14. A spinner has 4 equal sections. What is the theoretical probability of the spinner stopping on section 2? What is the sample space? 15. Is it possible for an event to have a probability of 1? Explain your answer. Probability of Simple Events: HOMEWORK

You are rolling a standard number cube. Find the theoretical probability of each outcome.

16. P(rolling a 2) 17. P(rolling a 3)

18. P(rolling an odd number) 19. P(rolling a 7)

20. P(rolling a multiple of 2)

1 2

4 3


A bag contains 1 red marble, 5 green marbles, 1 blue marble, and 1 yellow marble. Suppose one marble is picked at random. Find each probability. 21. P(blue) 22. P(not yellow)

23. P(red or green) 24. P(green)

Two standard number cubes are rolled. Find each probability.

25. P(a sum equal to 3) 26. P(a sum not equal to 3)

27. P(a product equal to 15) 28. P(a sum greater than 6) 29. A game is played where students throw beanbags at the target

shown to the right. Each region of the target is the same size and every beanbag hits the target. What is the theoretical probability of hitting section D? What is the sample space?

30. An event has a probability of 0. What does this tell you about the event? Explain.

A

B C D


Probability and Length: CLASSWORK

Find the probability that a point chosen at random from 𝐴𝐾̅̅ ̅̅ is on the given segment.

31. 𝐶𝐹̅̅̅̅

32. 𝐵𝐼̅̅ ̅

33. 𝐺𝐾̅̅ ̅̅

34. 𝐹𝐺̅̅ ̅̅

35. 𝐴𝐾̅̅ ̅̅

36. 𝐴𝐶̅̅ ̅̅

A point between A and B on each number line is chosen at random. What is the probability that the point is between C and D?

37. 38.

39. Roberto’s trolley runs every 45 minutes. If he arrives at the trolley stop at a random time, what is the probability that he will not have to wait more than 10 minutes?

40. Suppose that your school day begins at 7:30 am and ends at 3:00 pm. You eat lunch at 11:00 am. If there is a fire drill at a random time during the day, what is the probability that it is before lunch?


Probability and Length: HOMEWORK

Find the probability that a point chosen at random from 𝐴𝐾̅̅ ̅̅ is on the given segment.

41. 𝐶𝐺̅̅ ̅̅

42. 𝐵𝐻̅̅ ̅̅

43. 𝐴𝐺̅̅ ̅̅

44. 𝐴𝐵̅̅ ̅̅

45. 𝐴𝐽̅̅ ̅

46. 𝐷𝐹̅̅ ̅̅

A point between A and B on each number line is chosen at random. What is the probability that the point is between C and D?

47. 48.

49. A stoplight at an intersection stays red for 60 seconds, changes to green for 45 seconds, and then turns yellow for 15 seconds. If Jamal arrives at the intersection at a random time, what is the probability that he will have to wait at a red light?

50. You are expecting a call from a friend anytime between 6:00 pm and 7:00 pm. Unexpectedly you have to leave your house to run an errand from 5:45 to 6:10 pm. What is the probability that you missed your friend’s call?


Probability and Area: CLASSWORK

A point in the figure is chosen at random. Find the probability that the point

lies in the shaded region.

51. 52. 53.

Use the dartboard at the right for 54–56. Assume that a dart you throw will land on the dartboard and is equally likely to land at any point on the board. The radii of the concentric circles are 4 in, 6 in, and 8 in respectively.

54. What is the probability of hitting region X?

55. What is the probability of hitting region Y?

56. What is the probability of hitting region Z?


Darts are thrown at each of dartboards below. A dart hits the board at a random point. Judging by appearance, find the probability that it will land in the shaded region. 57. 57. 58. 59.

Probability and Area: HOMEWORK

A point in the figure is chosen at random. Find the probability that the point

lies in the shaded region.

60. 61. 62.


Use the dartboard at the right for 63–65. Assume that a dart you throw will land on the dartboard and is equally likely to land at any point on the board. The radii of the concentric circles are 3 in, 6 in, and 9 in respectively.

63. What is the probability of hitting region X?

64. What is the probability of hitting region Y?

65. What is the probability of hitting region Z?

Darts are thrown at each of dartboards below. A dart hits the board at a random point. Judging by appearance, find the probability that it will land in the shaded region. 66. 67. 68.


Review: Probability

Find the probability that a point J, selected randomly on 𝐴𝐹̅̅ ̅̅ , is on the given segment.

1. 𝐴𝐵̅̅ ̅̅ ____________ 2. 𝐶𝐷̅̅ ̅̅ ____________

3. 𝐵𝐷̅̅ ̅̅ ____________ 4. 𝐶𝐹̅̅̅̅ ____________ 5. The school day consists of four block classes, each 90 minutes long. Lunch is 30 minutes. Passing time between classes and/or lunch is 5 minutes. If there is a fire drill at a random time during the day, what is the probability that it begins during lunch? 6. You have planned to meet your friend at the mall at 4 P.M. The city bus runs every 10 minutes and the trip to the store is 6 minutes. You arrive at the bus stop at 3:50 P.M. What is the probability that you will arrive at the mall by 4 P.M.? 7. The school day begins at 7:00 A.M. and ends at 2:30 P.M. You have math class, and it ends at 12:30 P.M. If there is a fire drill at a random time during the day, what is the probability that it begins after math class?

Find the probability that a randomly chosen point in the figure lies in the shaded region. Round to the nearest tenth of a percent. 8.


9.

10.

11.

12. A square target with 20 cm sides includes a triangular region with equal side lengths of 5 cm. A dart is thrown and hits the target a random. Find the probability that the dart hits the triangle.


13. Find the probability for each outcome on the game spinner below.

a. Receive 20 points

b. Move 2 spaces

c. Free turn

d. Lose 5 points

e. Lose a turn


Answer Key

1. 1

6

2. 1

6

3. 1

2

4. 1

6

5. 1

3

6. 1

3

7. 2

3

8. 5

9

9. 2

9

10. 1

36

11. 35

36

12. 1

12

13. 1

36

14. 1

4, {1, 2, 3, 4}

15. Yes there is a 100% chance that

the event will happen.

16. 1

6

17. 1

6

18. 1

2

19. 0

20. 1

2

21. 1

8

22. 7

8

23. 3

4

24. 5

8

25. 1

18

26. 17

18

27. 1

18

28. 7

12

29. 1

4, {𝐴, 𝐵, 𝐶, 𝐷}

30. There is no chance that the event

can happen.

31. 3

10

32. 7

10

33. 2

5

34. 1

10


35. 1

36. 1

5

37. 1

5

38. 3

5

39. 2

9

40. 3

7

41. 2

5

42. 3

5

43. 3

5

44. 1

10

45. 9

10

46. 1

5

47. 1

5

48. 1

3

49. 1

2

50. 1

6

51. 3𝜋

4

52. 1

10

53. 12

25𝜋

54. 𝜋

36

55. 𝜋

16

56. 𝜋

9

57. 1

4

58. 1

2

59. 1

2

60. 48−36𝜋

48

61. 3

20

62. 9

32𝜋

63. 𝜋

144

64. 𝜋

36

65. 𝜋

16

66. 1

3

67. 2

5

68. 1

4


Review: Probability

1. 1/6 ≈ 16.7% 2. ¼ = 25%

3. 5/12 ≈ 42% 4. 2/3 ≈ 66.7%

5. 3/41 ≈ 7.3% 6. 2/5 = 40%

7. 4/15 ≈ 26.7%

8. 21.5% 9. 74.3% 10. 80% 11. 18.8%

12. sqrt(3) / 64 ≈ 2.7% 13.

a. 1/12 ≈ 8.3%

b. 7/36 ≈ 19.4% c. ¼ = 25%

d. 1/12 ≈ 8.3% e. 7/18 ≈ 38.9%

new probability probability of simple events: classwork 1. p 2. p...

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