Use a Simulation

1. Use a Simulation 9.3 Pre-Algebra

2. 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. Learn to use a simulation to estimate probability.

4. Vocabulary simulation random numbers

5. 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.

6. 1 Understand the Problem Example: 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. 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.

7. Make a Plan 2 Example 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.

8. Make a Plan 2 Example Continued

9. 3 Solve Example Continued Starting on the third row of the table from the previous slide and using 10 digits for each trial yields the data at right:

10. 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 4 Look Back Example Continued 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.

11. 1 Understand the Problem Try This 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. 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%.

12. Make a Plan 2 Try This 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.

13. 3 Solve Try This Continued 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

14. 4 Look Back Try This 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% 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.

15. Lesson Quiz Use the table of random numbers to simulate the situation. 2 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. 2 6 Possible answer: 30%