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Unlocking Probability Through Simulation: Engaging Math Lesson**

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16 diapositives · 319 Views · Jul 27, 2014

This lesson focuses on utilizing simulations to estimate probabilities in real-world scenarios. Students will learn to apply simulations to problems, such as estimating the probability of a random selection or outcomes from repeated trials, exemplified by using random numbers to model events like a dart player's success rate. The lesson includes warm-up problems, practical applications, and quizzes to reinforce understanding. By the end, students will grasp the significance of simulations in estimating probabilities and interpreting results accurately.**

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Unlocking Probability Through Simulation: Engaging Math Lesson**
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  1. 9-3 Use a Simulation Course 3 Warm Up Problem of the Day Lesson Presentation

  2. 9-3 Use a Simulation Course 3 • 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. 9-3 Use a Simulation Course 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. 9-3 Use a Simulation Course 3 Learn to use a simulation to estimate probability.

  5. 9-3 Use a Simulation Course 3 Insert Lesson Title Here Vocabulary simulation random numbers

  6. 9-3 Use a Simulation Course 3 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. 9-3 Use a Simulation 1 Understand the Problem Course 3 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. 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. 9-3 Use a Simulation Make a Plan 2 Course 3 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.

  9. 9-3 Use a Simulation Make a Plan 2 Course 3 Additional Example 1 Continued

  10. 9-3 Use a Simulation 3 Solve Course 3 Additional Example 1 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:

  11. 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 4 Look Back Course 3 Additional Example 1 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.

  12. 9-3 Use a Simulation 1 Understand the Problem Course 3 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. 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. 9-3 Use a Simulation Make a Plan 2 Course 3 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.

  14. 9-3 Use a Simulation 3 Solve Course 3 Try This: Example 1 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

  15. 9-3 Use a Simulation 4 Look Back Course 3 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% 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. 9-3 Use a Simulation Course 3 Insert Lesson Title Here Lesson Quiz Use the table of random numbers to simulate the situation. 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. Possible answer: 30%