1. Using Simulation to Estimate Probabilities
Section 5.2 Day 2
Using Simulation to Estimate Probabilities

2. 4 Steps to Use Simulations
State your assumptions

3. 4 Steps to Use Simulations
State your assumptions
2. Describe how you will use random digits to conduct one run of the simulation

4. 4 Steps to Use Simulations
State your assumptions
Describe how you will use random digits to conduct one run of the simulation
Run the simulation a large number of times, recording the results in a frequency table

5. 4 Steps to Use Simulations
State your assumptions
Describe how you will use random digits to conduct one run of the simulation
Run the simulation a large number of times, recording the results in a frequency table
Write a conclusion in the context of the situation

6. Page 312, E16

7. Page 312, E16
Assumptions:

8. Page 312, E16
Assumptions:
each boy selected has an 18% chance of reporting that he rarely or never wears a seat belt

9. Page 312, E16
Assumptions:
each boy selected has an 18% chance of reporting that he rarely or never wears a seat belt
the boys are selected independently of each other

10. E16
Model?

11. E16 Boys who say they rarely or never wear a seat belt:
Boys who say something else:

12. E16 Boys who say they rarely or never wear a seat belt: 01 - 18
Boys who say something else: 19–99, 00

13. E16 You are looking for the probability, in a sample of 9
boys, that 0 boys will say they rarely or never wear
a seat belt.
Select nine pairs of digits, allowing repeats, and
record whether or not each pair represents a boy
who says he rarely or never wears a seat belt.

14. E16 You are looking for the probability, in a sample of 9
boys, that 0 boys will say they rarely or never wear
a seat belt.
Select nine pairs of digits, allowing repeats, and
record whether or not each pair represents a boy
who says he rarely or never wears a seat belt.
Count the number out of 9 who say they rarely
or never wear a seat belt.

15. E16
Repetition: Begin with Row 41 of Table D and conduct the first run of the simulation.

16. E16
Repetition: Begin with Row 41 of Table D. Pairs of digits separated.
Each pair represents 1 boy
Boys who say they rarely or never wear a seat belt:

17. E16
Repetition: Begin with Row 41 of Table D. Pairs of digits separated.
Boys who say they rarely or never wear a seat belt: 2

18. Perform the next two runs of the simulation

19. E16 2 2 4
Boys who say they rarely or never wear
a seat belt:

20. E16

21. E16
Update the table with our 10 runs.

22. E16

23. E16
Conclusion:

24. E16 Conclusion: The estimated probability is ________ that a
random sample of 9 boys will contain none
who say they use their seat belt rarely or
never.

25. E16 Conclusion: The estimated probability is or about
0.16, that a random sample of 9 boys will
contain none who say they use their seat
belt rarely or never.

26. Page 312, E17
Assumptions:

27. Page 312, E17
Assumptions:
You have a 25% chance of being correct on each question

28. Page 312, E17
Assumptions:
You have a 25% chance of being correct on each question and
Your answer to each question is
independent of your answers to the other
questions.

29. Page 312, E17
Model:

30. Page 312, E17
Model:
Correct response:
Incorrect response:

31. Page 312, E17 Model: Correct response: 01–25
Incorrect response: 26–99, 00

32. Page 312, E17
Model:
A single run consists of selecting ten pairs of digits
to represent the ten questions, so select ten pairs
of digits, allowing repeats, and record whether the
pair represents a correct or incorrect response.
Record the number of correct responses for
each run.

33. Another Possible Model
Disregard digits 8 and 9.
A single run consists of selecting ten digits to represent the ten questions, so select ten digits, allowing repeats, and record whether the digit represents a correct or incorrect response. Record the number of correct responses for each run.
Correct response
0, 1
Incorrect response
2, 3, 4, 5, 6, 7,

34. Page 312, E17 Let’s use this model: Correct response: 01–25
Incorrect response: 26–99, 00
Do two runs.

35. Page 312, E17 Let’s use this model: Correct response: 01–25
Incorrect response: 26–99, 00 4 2

36. Page 312, E17

37. Page 312, E17

38. Page 312, E17
The estimated probability of answering half or more of the questions correctly is ?

39. Page 312, E17
Conclusion: The estimated probability of answering half or more of the questions correctly is

40. Page 299, E5
Using a two-way table, show all possible equally likely outcomes if two fair tetrahedral dice are rolled.

41. Page 299, E5

43. Disjoint? Complete?
a. {no 4 on the two rolls, one 4, two 4’s}

44. Disjoint? Complete?
a. {no 4 on the two rolls, one 4, two 4’s}

45. Disjoint? Complete?
b. {the first roll is a 4, the second roll is a 4, neither roll is a 4}

46. Disjoint? Complete?
b. {the first roll is a 4, the second roll is a 4, neither roll is a 4}

47. Disjoint? Complete?
c. {the first 4 comes on the first roll, the first 4 comes on the second roll}

48. Disjoint? Complete?
c. {the first 4 comes on the first roll, the first 4 comes on the second roll}

49. Disjoint? Complete?
d. {the sum of the two rolls is less than 2, the sum is more than 2}

50. Disjoint? Complete?
d. {the sum of the two rolls is less than 2, the sum is more than 2}

51. Disjoint? Complete?
e. {the first roll is a 4, neither roll is a 4}

52. Disjoint? Complete?
e. {the first roll is a 4, neither roll is a 4}

53. Questions?