1. 9-3 Use a Simulation Warm Up Problem of the Day Lesson Presentation
Pre-Algebra

2. 9-3 Use a Simulation Warm Up 0.12 0.52
Pre-Algebra
9-3
Use a Simulation
Warm Up
1. There are 25 out of 216 sophomores enrolled in a physical-education course. Estimate the probability that a randomly selected sophomore is enrolled in a physical-education course.
2. A spinner was spun 230 times. It landed on red 120 times, green 65 times, and yellow 45 times. Estimate the probability of its landing on red.
0.12
0.52

3. Problem of the Day
If a triangle is worth 7 and a rectangle is worth 8, how much is a hexagon worth? 10

4. Learn to use a simulation to estimate probability.

5. Vocabulary
simulation
random numbers

6. A simulation is a model of a real situation
A simulation is a model of a real situation. In a set of random numbers, each number has the same probability of occurring as every other number, and no pattern can be used to predict the next number. Random numbers can be used to simulate random events in real situations.

7. Understand the Problem
Additional Example 1: Problem Solving Application
A dart player hits the bull’s-eye 25% of the times that he throws a dart. Estimate the probability that he will make at least 2 bull’s-eyes out of his next 5 throws. 1
Understand the Problem
The answer will be the probability that he will make at least 2 bull’s-eyes out of his next 5 throws.
List the important information:
The probability that the player will hit the bull’s-eye is 0.25.

8. Additional Example 1 Continued2
Make a Plan
Use a simulation to model the situation. Use digits grouped in pairs. The numbers 01–25 represent a bull’s-eye, and the numbers 26–00 represent an unsuccessful attempt. Each group of 10 digits represent one trial.

9. Additional Example 1 Continued2
Make a Plan

10. Additional Example 1 Continued
Solve 3
Starting on the third row of the table from the previous slide and using 10 digits for each trial yields the data at right:

11. Additional Example 1 Continued
Out of the 10 trials, 2 trials represented two or more bull’s-eyes. Based on this simulation, the probability of making at least 2 bull’s-eyes out of his next 5 throws is about , or 20%. 2 10
Look Back 4
Hitting the bull’s-eye at a rate of 20% means the player hits about 20 bull’s-eye out of every 100 throws. This ratio is equivalent to 2 out of 10 throws, so he should make at least 2 bull’s-eyes most of the time. The answer is reasonable.

12. Understand the Problem
Try This: Example 1
Tuan wins a toy from the toy grab machine at the arcade 30% of the time. Estimate the probability that he will win a toy 1 time out of the next 3 times he plays. 1
Understand the Problem
The answer will be the probability that he will win 1 of the next 3 times.
List the important information:
The probability that Tuan will win is 30%.

13. Try This: Example 1 Continued2
Make a Plan
Use a simulation to model the situation. Use digits grouped in pairs. The numbers 01–30 represent a win, and the numbers 31–00 represent an unsuccessful attempt. Each group of 6 digits represent one trial.

14. Try This: Example 1 Continued86 58 52 79 19 65 26 49 35 57 94 42 51 33 25 16 63 85 84 18 39 47 32 66 67 89 93 87 83
Solve 3
1 win
Starting on the fourth row of the table from slide 3 and using 6 digits for each trial yields the data at right:
1 win
1 win
1 win

15. Try This: Example 1 Continued
Out of the 10 trials, 4 trials represented one or more wins. Based on this simulation, the probability of winning at least 1 time out of his next 3 games is 40%
Look Back 4
Winning at a rate of 40% means that Tuan wins about 40 times out of every 100 games. This ratio is equivalent to 4 out of 10 games, so he should win at least 4 toys most of the time. The answer is reasonable.

16. Use the table of random numbers to simulate the situation.
Lesson Quiz
Use the table of random numbers to simulate the situation.
38094
76211
43659
29272
76005
93391
19587
47380
33442
40809
27904
95412
69632
48461
25654
55889
42231
39983
13802
24483
52730
15604
80949
46351
10580
59765
76431
38586
62987
40440
93594
30198
64926
17672
68735
35168
19085
35497
30798
21966
Lydia gets a hit 34% of the time she bats. Estimate the probability that she will get at least 4 hits in her next 10 at bats.