12-6

1. Making Predictions 12-6 Course 1 Warm Up Problem of the Day Lesson Presentation

2. Making Predictions 12-6 1 1 __ ___ 4 36 Course 1 Warm Up 1.Zachary rolled a fair number cube twice. Find the probability of the number cube showing an odd number both times. 2. Larissa rolled a fair number cube twice. Find the probability of the number cube showing the same number both times.

3. Making Predictions 12-6 Course 1 Problem of the Day The average of three numbers is 45. If the average of the first two numbers is 47, what is the third number? 41

4. Making Predictions 12-6 Course 1 Learn to use probability to predict events.

5. Making Predictions 12-6 Course 1 Insert Lesson Title Here Vocabulary prediction population sample

6. Making Predictions 12-6 Course 1 Insert Lesson Title Here A prediction is a guess about something in the future. One way to make a prediction is to collect information by conducting a survey. The population is the whole group being surveyed. To save time and money; researchers often make predictions based on a sample, which is part of the group being surveyed. Another way to make a prediction is to use probability.

7. Making Predictions 12-6 Course 1 Additional Example 1: Using Sample Surveys to Make Prediction A store claims that 78% of shoppers end up buying something. Out of 1,000 shoppers, how many would you predict will buy something? You can write a proportion. Remember that percent means “per hundred.”

8. Making Predictions 12-6 x = 1,000 = 78,000 100x 78 ______ ___ ____ 100 100 100 Divide both sides by 100 to undo the multiplication. Think: 78 out of 100 is how many out of 1,000. The cross products are equal. x is multiplied by 100. Course 1 Additional Example 1 Continued 100 •x = 78 • 1,000 100x = 78,000 x = 780 You can predict that about 780 out of 1,000 customers will buy something.

9. Making Predictions 12-6 Course 1 Check It Out: Example 1 A store claims 62% of shoppers end up buying something. Out of 1,000 shoppers, how many would you predict will buy something? You can write a proportion. Remember that percent means “per hundred.”

10. Making Predictions 12-6 x = 1,000 = 62,000 100x 62 ______ ___ ____ 100 100 100 Divide both sides by 100 to undo the multiplication. Think: 62 out of 100 is how many out of 1,000. The cross products are equal. x is multiplied by 100. Course 1 Check It Out: Example 1 Continued 100 •x = 62 • 1,000 100x = 62,000 x = 620 You can predict that about 620 out of 1,000 customers will buy something.

11. Making Predictions 12-6 P(greater than 2) = = 2 4 __ __ 3 6 = x 2 ___ __ 30 3 The cross products are equal. Think: 2 out of 3 is how many out of 30. x is multiplied by 3. Course 1 Additional Example 2: Using Theoretical Probability to Make Predictions If you roll a number cube 30 times, how many times do you expect to roll a number greater than 2? 3 •x = 2 • 30 3x = 60

12. Making Predictions 12-6 = 3x 60 __ __ 3 3 Divide both sides by 3 to undo the multiplication. Course 1 Additional Example 2 Continued x = 20 You can expect to roll a number greater than 2 about 20 times.

13. Making Predictions 12-6 P(greater than 3) = = 1 3 __ __ 2 6 = x 1 ___ __ 30 2 The cross products are equal. Think: 1 out of 2 is how many out of 30. x is multiplied by 2. Course 1 Check It Out: Example 2 If you roll a number cube 30 times, how many times do you expect to roll a number greater than 3? 2 •x = 1 • 30 2x = 30

14. Making Predictions 12-6 = 2x 30 __ __ 2 2 Divide both sides by 2 to undo the multiplication. Course 1 Check It Out: Example 2 Continued x = 15 You can expect to roll a number greater than 3 about 15 times.

15. Making Predictions 12-6 Course 1 Additional Example 3: Problem Solving Application Suppose the managers of a second stadium, like the one in the student book, also sell yearly parking passes. The managers of the second stadium estimate that the probability of a person with a pass attending any one event is 50%. The parking lot has 400 spaces. If the managers want the lot to be full at every event, how many passes should they sell?

16. Making Predictions 12-6 1 Make a Plan Understand the Problem 2 Course 1 • The answer will be the number of parking passes they should sell. • List the important information: • P(person with pass attends event): = 50% • There are 400 parking spaces The managers want to fill all 400 spaces. But on average, only 50% of parking pass holders will attend. So 50% of pass holders must equal 400. You can write an equation to find this number.

17. Making Predictions 12-6 3 Solve = = 400 50x 50 40,000 ____ ___ ______ ___ x 50 50 100 The cross products are equal. Think: 50 out of 100 is 400 out of how many? Divide both sides by 50 to undo the multiplication. x is multiplied by 50. Course 1 100 • 400 = 50 •x 40,000 = 50x 800 = x The managers should sell 800 parking passes.

18. Making Predictions 12-6 Look Back 4 Course 1 Insert Lesson Title Here If the managers sold only 400 passes, the parking lot would not usually be full because only about 50% of the people with passes will attend any one event. The managers should sell more than 400 passes, so 800 is a reasonable answer.

19. Making Predictions 12-6 Course 1 Check It Out: Example 3 The concert hall managers sell annual memberships. If you have an annual membership, you can attend any event during that year. The managers estimate that the probability of a person with a membership attending any one event is 60%. The concert hall has 600 seats. If the managers want the seats to be full at every event, how many memberships should they sell?

20. Making Predictions 12-6 1 Make a Plan Understand the Problem 2 Course 1 • The answer will be the number of membership they should sell. • List the important information: • P(person with membership attends event): = 60% • There are 600 seats The managers want to fill all 600 seats. But on average, only 60% of membership holders will attend. So 60% of membership holders must equal 600. You can write an equation to find this number.

21. Making Predictions 12-6 3 Solve = = 600 60x 60 60,000 ____ ___ ______ ___ x 60 60 100 The cross products are equal. Think: 60 out of 100 is 600 out of how many? Divide both sides by 60 to undo the multiplication. x is multiplied by 60. Course 1 100 • 600 = 60 •x 60,000 = 60x 1,000 = x The managers should sell 1,000 annual memberships.

22. Making Predictions 12-6 Look Back 4 Course 1 Insert Lesson Title Here If the managers sold only 600 annual memberships, the seats would not usually be full because only about 60% of the people with memberships will attend any one event. The managers should sell more than 600 passes, so 1,000 is a reasonable answer.

23. Making Predictions 12-6 Course 1 Insert Lesson Title Here Lesson Quiz: Part I 1. The owner of a local pizzeria estimates that 72% of his customers order pepperoni on their on their pizza. Out of 250 orders taken in one day, how many would you predict to have pepperoni? 180

24. Making Predictions 12-6 Course 1 Insert Lesson Title Here Lesson Quiz: Part II 2. A bag contains 9 red chips, 4 blue chips, and 7 yellow chips. You pick a chip from the bag, record its color, and put the chip back in the bag. If you do this 100 times, how many times do you expect to remove a yellow chip from the bag? 3. A quality-control inspector has determined that 3% of the items he checks are defective. If the company he works for produces 3,000 items per day, how many does the inspector predict will be defective? 35 90