Skill Review Unique has a bag of marbles

Skill Review Unique has a bag of marbles. There are 4 colors of marbles: red, blue, yellow, and green. The table shows the frequencies of marbles after drawing from the bag 50 times. Color Frequency Red 9 Blue 23 Green 11 What is the probability Unique chooses a yellow marble? a. 14 % c. 22 % b. 18 % d. 46 %

Have you ever tried to predict which football team will win a big game? If so, you probably did not just pick the team with the coolest colors or the neatest mascot. You may have based your pick on statistics about win‑loss records, player injuries, and other data. Knowing what has happened in the past can sometimes help you predict what will happen in the future. In this lesson, you will use data to make predictions.

As you work with your team to come up with hypotheses of what the mystery spinner looks like, keep the questions below in mind: • What is the probability or likelihood? • What do we expect to happen? • How does the actual event compare to our prediction? • What can we know for sure?

1 -63. THE MYSTERY SPINNER Your teacher has a hidden spinner. 0. 0 Your challenge is to perform an experiment that will allow you to predict what the spinner looks like without ever seeing it. Your Task: Your teacher will spin the spinner and announce each result. During the experiment, you will consider several questions about the results and about the hidden spinner. However, you will not be allowed to see it. Using the information you get, work with your team to figure out what the spinner looks like. When you think you know what it looks like, draw a diagram of the spinner.

1 -63. THE MYSTERY SPINNER a. Based on your data, how can you describe the likelihood of landing on each part of the spinner? How does the spinner that you drew represent these likelihoods? Be prepared to share your ideas. b. Use your data to write the experimental probability of each of the following results as a fraction, a decimal, and a percent. i. The spinner lands on purple. ii. The spinner lands on green or orange.

1 -63. THE MYSTERY SPINNER c. If your teacher were to spin the spinner 15 more times, would this change the likelihood from answers in part (b)? d. Do you know for sure that the spinner you drew looks exactly like your teacher’s? Are you certain that the portions that you drew for each color are the same size as the portions on your teacher’s spinner? Why or why not?

1 -64. Now your teacher will reveal the mystery spinner. a. How does your team’s spinner compare to the actual spinner? Discuss the similarities and differences. a. Does your spinner and your teacher’s spinner show the same likelihood for each section being spun? Explain why or why not.

1 -66. One way to compare your spinner and your teacher’s spinner is to calculate theoretical probability for each colored section of your teacher’s spinner. a. What are some reasons the experimental probability and theoretical probability for any section of the spinner could be different? b. Estimate theoretical probability for getting each color on your teacher’s spinner. c. How does the experimental probabilities (based on your class data) and theoretical probabilities (based on the actual spinner) compare? How do you think they would compare if there were twice as many spins made? What about three times as many spins?

d. If you were to spin the spinner the number of times listed below, how many times would you expect it to land on orange? Explain how you found your answers. i. 6 times ii. 48 times e. Approximately how many times would you expect to land on orange if you were to spin 100 times?

b. Rachel and Christie flip a coin every evening for the first week. Christie has washed the dishes four times, and Rachel has washed the dishes three times. Christie tells Rachel that the system is not fair, because Christie has done the dishes more often than Rachel. Is Christie right? c. After the second week of coin flipping, Christie has washed the dishes ten times and Rachel has washed the dishes four times. Now Christie is really upset at Rachel because she has washed the dishes so many times. d. With the new information, do you think the system is fair or not fair? What would you recommend to Christie?

Practice 1. What is the likelihood of pulling a blue marble out of a bag of green marbles? 2. What is the likelihood that there are students in your classroom that will be at school each day this year? 3. What is the likelihood of landing on an odd number when the spinner is labeled with numbers 1 – 10? 4. What is the likelihood that the students in your school like chocolate ice cream? 5. What is the likelihood that your teacher will be at school tomorrow?