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

Making Predictions 12-6 Warm Up Course 1 12-6 Making Predictions 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. 1 4 __ 1 36 ___

Making Predictions 12-6 Problem of the Day Course 1 12-6 Making Predictions 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

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

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

Insert Lesson Title Here Course 1 12-6 Making Predictions 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.

Additional Example 1: Using Sample Surveys to Make Prediction Course 1 12-6 Making Predictions 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.”

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

Making Predictions 12-6 Check It Out: Example 1 Course 1 12-6 Making Predictions 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.”

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

Course 1 12-6 Making Predictions 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? P(greater than 2) = = 4 6 __ 2 3 2 3 __ x 30 ___ = Think: 2 out of 3 is how many out of 30. The cross products are equal. 3 • x = 2 • 30 x is multiplied by 3. 3x = 60

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

Making Predictions 12-6 Check It Out: Example 2 Course 1 12-6 Making Predictions 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? P(greater than 3) = = 3 6 __ 1 2 1 2 __ x 30 ___ = Think: 1 out of 2 is how many out of 30. The cross products are equal. 2 • x = 1 • 30 x is multiplied by 2. 2x = 30

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

Additional Example 3: Problem Solving Application Course 1 12-6 Making Predictions 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?

Understand the Problem Course 1 12-6 Making Predictions 1 Understand the Problem 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 2 Make a Plan 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.

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

Insert Lesson Title Here Course 1 12-6 Making Predictions Insert Lesson Title Here Look Back 4 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.

Making Predictions 12-6 Check It Out: Example 3 Course 1 12-6 Making Predictions 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?

Understand the Problem Course 1 12-6 Making Predictions 1 Understand the Problem 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 2 Make a Plan 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.

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

Insert Lesson Title Here Course 1 12-6 Making Predictions Insert Lesson Title Here Look Back 4 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.

Insert Lesson Title Here Course 1 12-6 Making Predictions 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

Insert Lesson Title Here Course 1 12-6 Making Predictions 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