Preview Warm Up California Standards Lesson Presentation

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 a 3 both times. 1 4 __ 1 36 ___

California Standards SDAP3.2 Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven). Also covered: NS1.3, SDAP3.3

Vocabulary prediction

A prediction is a guess about something in the future A prediction is a guess about something in the future. Suppose you know the experimental probability that an airline’s flight will be on time. You can use the probability to predict how many flights out of 1,000 will be on time.

Additional Example 1: Using Experimental Probability to Make Predictions 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 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 100x = 78,000 100x 100 ____ 78,000 ______ = Divide both sides by 100. x = 780 You can predict that about 780 out of 1,000 customers will buy something.

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 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 100x = 62,000 100x 100 ____ 62,000 ______ = Divide both sides by 100. x = 620 You can predict that about 620 out of 1,000 customers will buy something.

Think: 2 out of 3 is how many out of 30? 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 3x = 60 3x 3 __ 60 = Divide both sides by 3. x = 20

Additional Example 2 Continued If you roll a number cube 30 times, how many times do you expect to roll a number greater than 2? You can expect to roll a number greater than 2 about 20 times.

Think: 1 out of 2 is how many out of 30? 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 2x 2 __ 30 = Divide both sides by 2. x = 15

Check It Out! Example 2 Continued If you roll a number cube 30 times, how many times do you expect to roll a number greater than 3? You can expect to roll a number greater than 3 about 15 times.

Additional Example 3: Problem Solving Application Suppose the managers of a second stadium, like the one on page 411, 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 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.

Think: 50 out of 100 is 400 out of how many? 50 100 ___ 400 x ____ 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 40,000 = 50x 40,000 50 ______ 50x ___ = Divide both sides by 50. 800 = x The managers should sell 800 parking passes.

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.

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 manager estimates that the probability of a person with a membership attending any one event is 60%. The concert hall has 600 seats. If the manager want the seats to be full at every event, how many memberships should she sell?

Understand the Problem 1 Understand the Problem The answer will be the number of memberships they should sell. List the important information: P(person with membership attends event): = 60% There are 600 seats 2 Make a Plan The manager wants 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.

Think: 60 out of 100 is 600 out of how many? 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 60,000 = 60x 60,000 60 ______ 60x ___ = Divide both sides by 60. 1,000 = x The manager should sell 1,000 annual memberships.

Look Back 4 If the manager 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.

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? about 180

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? about 35 about 90