10-3 Use a Simulation Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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 Course 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 Course Use a Simulation

Learn to use a simulation to estimate probability. Course Use a Simulation

Vocabulary simulation random numbers Insert Lesson Title Here Course Use a Simulation

Course 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.

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 Course Use a Simulation 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.

Additional Example 1 Continued Course Use a Simulation 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. 2 Make a Plan

Course Use a Simulation Starting on the third row of the table of p. 532 and using 10 digits for each trial yields the data at right: Solve 3 Additional Example 1 Continued

Course Use a Simulation Additional Example 1 Continued Calculators and computers can generate sets of approximately random numbers. A formula is used to generate the numbers, so they are not truly random, but they work for most simulations. Helpful Hint

Course 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% Look Back4 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

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. Check It Out: Example 1 Course Use a Simulation 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%.

Check It Out: Example 1 Continued Course Use a Simulation 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. 2 Make a Plan

Course Use a Simulation Starting on the fourth row of the table on p. 532 and using 6 digits for each trial yields the data at right: Solve 3 Check It Out: Example 1 Continued win

Course 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 Back4 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. Check It Out: Example 1 Continued

Lesson Quiz Use the table of random numbers to simulate the situation. Possible answer: 30% Insert Lesson Title Here Course Use a Simulation 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.