Foundations to Algebra In Class: Investigating Probability
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1 Foundations to Algebra In Class: Investigating Probability Name Date How can I use probability to make predictions? 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 uncover a mystery spinner, 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. The Mystery Spinner Your teacher has a hidden spinner. 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 abut 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 below. Results Diagram Color Tallies
2 2. Use the data you collected in Problem 1 to answer the following questions. a. 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. P(purple) = ii. The spinner lands on green. P(green) = iii. The spinner lands on blue. P(blue) = iv. The spinner lands on orange. P(orange) = b. If your teacher were to spin the spinner 15 more times, how might this change you answers for part (a)? c. Do you know for sure that the spinner you drew in Problem 1 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? 3. 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. b. Do your spinner and your teacher s spinner show the same likelihood for each section being spun? Explain why or why not. 4. One way to compare your spinner and your teacher s spinner is to calculate the theoretical probability for each colored section of your teacher s spinner. a. Find the theoretical probability for getting each color on your teacher s spinner. b. What are some reasons the experimental probability and the theoretical probability for any section of the spinner could be different?
3 c. How do the experimental probabilities (based on your class data) and the 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? How can you express the probability of landing on orange as a percent? 5. You will think about theoretical probability more in parts (a) through (e) below. It will help you to know that a standard deck of 52 playing cards has four suits: spades and clubs, which are black, and hearts and diamonds, which are red. Each suit has 13 cards: cards numbered 2 through 10, three face cards (a jack, a queen, and a king), and an ace. It will also be helpful to know that a standard number cube, also called a die (plural: dice), has six sides. Each side has a different number of dots, 1 through 6. Look at the situations below and decide with your team if you can find a theoretical probability for each one. If you decide that you can find the theoretical probability, then do so. a. Picking an ace from a standard 52-card deck. b. Not rolling a 3 on a standard number cube. c. The chances of a thumbtack landing with its point up or on its side. d. Getting the one red crayon from a set of eight different-color crayons. e. The likelihood that you will run out of gas on a long car trip.
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5 Foundations to Algebra Investigating Probability HOMEWORK Name Date Review and Preview 1. Imagine that you have a bag containing 10 marbles of different colors. You have drawn a marble, recorded its color and replaced if fifty times, with the following results: 9 purple, 16 orange, 6 yellow, and 19 green marbles. Make a prediction for how many marbles of each color are in the bag. Show all of your work or explain your reasoning. 2. A fair number cube with the numbers 1, 2, 3, 4, 5 and 6 is rolled. a. What is the theoretical probability of getting an even number? b. What is the theoretical probability of getting a factor of 6? 3. If 15 books cost $135, how much would 6 books cost? Explain your answer or show your work to receive full credit! 4. a. Explain in complete sentences how to find the next two terms in the sequence: 1, 1, 2, 3, 5, 8, 13 b. Find the next two terms in the sequence.
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