Pre-Algebra

9-3 Use a Simulation9-3 Use a Simulation

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

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

Pre-Algebra

9-3 Use a Simulation

Pre-Algebra

9-3 Use a Simulation

Problem of the Day

If a triangle is worth 7 and a rectangle is worth 8, how much is a hexagon worth?

10

Pre-Algebra

9-3 Use a Simulation

Learn to use a simulation to estimate probability.

Pre-Algebra

9-3 Use a Simulation

Vocabulary

simulationrandom numbers

Pre-Algebra

9-3 Use a Simulation

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.

Pre-Algebra

9-3 Use a Simulation

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.

Additional Example 1: Problem Solving Application

11 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.

Pre-Algebra

9-3 Use a Simulation

Additional Example 1 Continued

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.

22 Make a Plan

Pre-Algebra

9-3 Use a Simulation

Additional Example 1 Continued

22 Make a Plan

Pre-Algebra

9-3 Use a Simulation

Starting on the third row of the table from the previous slide and using 10 digits for each trial yields the data at right:

Solve33

Additional Example 1 Continued

Pre-Algebra

9-3 Use a Simulation

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 Back44

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.

Additional Example 1 Continued

Pre-Algebra

9-3 Use a Simulation

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.

Try This: Example 1

11 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%.

Pre-Algebra

9-3 Use a Simulation

Try This: Example 1 Continued

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.

22 Make a Plan

Pre-Algebra

9-3 Use a Simulation

Starting on the fourth row of the table from slide 3 and using 6 digits for each trial yields the data at right:

Solve33

Try This: Example 1 Continued

86 58 52

79 19 65

26 49 35

57 94 42

51 33 25

16 63 52

85 84 18

39 47 32

66 67 89

93 87 83

1 win

1 win

1 win1 win

Pre-Algebra

9-3 Use a Simulation

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 Back44

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.

Try This: Example 1 Continued

Pre-Algebra

9-3 Use a Simulation

Lesson QuizUse 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

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.