Main Idea and New Vocabulary Example 1: Experimental Probability Example 2: Experimental and Theoretical Probability Example 3: Experimental and Theoretical Probability Example 4: Predict Future Events Example 5: Predict Future Events Lesson Menu

Find and compare experimental and theoretical probabilities. theoretical probability experimental probability Main Idea/Vocabulary

Experimental Probability A spinner is spun 100 times and it lands on green 32 times. What is the experimental probability of spinning green? Answer: The experimental probability of the spinner landing on green is . Example 1

Two hundred pieces of candy are taken out of a bag Two hundred pieces of candy are taken out of a bag. Of those 200 pieces, 38 are caramels. What is the experimental probability of reaching into the bag and taking out a caramel? A. B. C. D. Example 1 CYP

Experimental and Theoretical Probability The graph below shows the results of an experiment in which a number cube is rolled 50 times. Find the experimental probability of rolling a 4. The graph indicates that a 1 was rolled 6 times, a 2 was rolled 12 times, a 3 was rolled 10 times, a 4 was rolled 9 times, a 5 was rolled 7 times, and a 6 was rolled 6 times. Example 2

Experimental and Theoretical Probability Answer: The experimental probability of rolling a 4 is Example 2

The graph below shows the results of an experiment in which a coin is flipped 20 times. Find the experimental probability of the coin coming up heads. A. B. C. D. Example 2 CYP

Experimental and Theoretical Probability The graph below shows the results of an experiment in which a number cube is rolled 50 times. Compare the experimental probability of rolling a 4 to its theoretical probability. Example 3

Experimental and Theoretical Probability The experimental probability is The number cube has 6 sides: 1, 2, 3, 4, 5 or 6. So, the theoretical probability of rolling a 4 is Since the experimental probability is close to the theoretical probability. Example 3

Experimental and Theoretical Probability Answer: The theoretical probability of rolling a 4 is Since , the experimental probability is close to the theoretical probability. Example 3

The graph below shows the results of an experiment in which a coin is flipped 20 times. Compare the experimental probability of the coin coming up heads to its theoretical probability. A. The experimental probability is close to the theoretical probability. B. The theoretical probability and experimental probability are the same. C. The experimental probability is not close to the theoretical probability. Example 3 CYP

There were 64 students and 12 chose hamburgers. So, the probability is Predict Future Events MEALS Mrs. Ramirez surveys her seventh-grade classes about what they are going to choose for lunch this week. Thirty students choose pizza, 17 students choose macaroni and cheese, 12 students choose hamburgers, and 5 choose chicken fingers. What is the experimental probability of someone choosing hamburgers? There were 64 students and 12 chose hamburgers. So, the probability is Answer: The experimental probability is Example 4

MUSIC Lisa surveyed her friends to see which type of music was their favorite. Four chose alternative, 8 chose rock, and 3 chose country. What is the experimental probability of one of Lisa’s friends choosing country music? A. B. C. D. Example 4 CYP

Predict Future Events MEALS Mrs. Ramirez surveys her seventh-grade classes about what they are going to choose for lunch this week. Thirty students choose pizza, 17 students choose macaroni and cheese, 12 students choose hamburgers, and 5 choose chicken fingers. Suppose Mrs. Ramirez surveys all 1,200 students in the school. How many students can she expect to choose hamburgers for lunch? Example 5

3  1,200 = 16  x Find the cross products. 3,600 = 16x Multiply. Predict Future Events Write a proportion. 3  1,200 = 16  x Find the cross products. 3,600 = 16x Multiply. 225 = x Divide each side by 16. Answer: 225 students Example 5

MUSIC Lisa surveyed her friends to see which type of music was their favorite. Four chose alternative, 8 chose rock, and 3 chose country. If Lisa surveys her entire class of 120 students how many can she expect to choose country as their favorite type of music? A. 124 students B. 123 students C. 40 students D. 24 students Example 5 CYP