What Do You Expect: Probability and Expected Value Name: Per: Investigation 2: Experimental and Theoretical Probability Date Learning Target/s Classwork Homework Self-Assess Your Learning Mon, Feb. 29 Leap Day! Analyze the fairness of a game by listing all possible outcomes in a tree diagram and determining theoretical probabilities. Pg. 2-3: WDYE 2.3: Designing a Fair Game Pg. 4: WDYE 2.3 Zaption Tues, Mar. 1 Analyze theoretical and experimental probabilities in a compound event. Pg. 5-6: WDYE 2.4: Winning the Bonus Prize Pg. 7: WDYE 2.4 Zaption Weds, Mar. 2 Use tree diagrams and the counting principle to find all possible outcomes. Pg. 8-9: Jesse James Puzzle Check Up Review Zaption Thurs, Mar. 3 Check Up Pg. 10: King s Puzzle Check Up 7.SP.C.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. 7.SP.C.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. 7.SP.C.7.B: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. 7.SP.C.8.A: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. 7.SP.C.8.B: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event. / / / / / Parent/Guardian Signature: Due: 1
WDYE 2.3: Designing a Fair Game Santo and Tevy are playing a game with coins. They take turns tossing three coins. If all three coins match, Santo wins. Otherwise, Tevy wins. Each player has won several turns in the game. Tevy, however, seems to be winning more often. Santo thinks the game is unfair. A game is a game in which all players have chances of winning. Santo drew the tree diagram to represent tossing three coins. A diagram is an illustration using branches to show the sample space of an event. The space is another name for the set of possible outcomes of an event. A. Use the tree diagram and answer the following questions: 1. What is the sample space for tossing three coins? (What are all of the possible outcomes?) 2. How many possible outcomes are three when you toss three coins? Are the outcomes equally likely? 3. What is the theoretical probability that the three coins will match? 4. What is the theoretical probability that exactly two coins will match? 5. Is the game played by Santo and Tevy a fair game? If so, explain why. If not, explain how to make it fair. 2
B. Suppose you tossed three coins for 24 trials. How many times would you expect two coins to match? C. Santo said, It is possible to toss three coins and have them match. Tevy replied, Yes, but is it probable? What do you think each boy meant? Challenge: Karen and Mia invent another game. They roll a number cube twice and read the digits shown as a two-digit number. So, if Karen gets a 6 and a 2, she has 62. a. Create a tree diagram for this situation. List all of the possible outcomes. b. What are all of the possible outcomes when you roll a number cube twice and create a two-digit number? c. What is the least number possible? d. What is the greatest number possible? e. Are all numbers equally likely? f. Suppose Karen wins on any prime number and Mia wins on any multiple of 4. Explain how to decide who is more likely to win. 3
WDYE 2.3: Homework Zaption 1. Patricia and Jean design a coin-tossing game. Patricia suggests tossing three coins. Jean says they can toss one coin three times. Are the outcomes different for the two situations? Explain. 2. Pietro and Eva are playing a game in which they toss a coin three times. Eva gets a point if no consecutive toss results match (as in HTH). Pietro gets a point if exactly two consecutive toss results match (as in HHT). If all three toss results match, no one scores a point. The first player to get 10 points wins. Is this a fair game? Explain. If it is not a fair game, change the rules to make it fair. 3. Silvia and Juanita are designing a game. A player in the game tosses two number cubes. Winning depends on whether the sum of the two numbers is odd or even. Silvia and Juanita make a tree diagram of possible outcomes. a. List all the outcomes for the sums. b. Design rules for a two-player game that is fair. c. Design rules for a two-player game that is not fair. d. How is this situation similar to tossing two coins and seeing if the coins match or don t match? 4
WDYE 2.4: Winning the Bonus Prize All the winners from the Gee Whiz Everyone Wins game show have the opportunity to compete for a bonus prize. Each winner chooses one block from each of two bags. Each bag contains one red, one yellow, and one blue block. This game consists of two events, which can also be called a event. The contestant must predict which color she or he will choose from each of the two bags. If the prediction is correct, the contestant wins a $10,000 bonus prize! What color choice gives you the best chance of winning? A. Conduct an experiment with 36 trials for the situation above. Record the pairs of colors that you choose. Trial Result Trial Result Trial Result Trial Result Trial Result 1 9 17 25 33 2 10 18 26 34 3 11 19 27 35 4 12 20 28 36 5 13 21 29 Pairs of Colors You Choose: 6 14 22 30 7 15 23 31 8 16 24 32 B. 1. Find the experimental probability of choosing each possible pair of colors. Use probability notation. 2. Make a tree diagram to show all of the possible pairs. List all of the possible outcomes. 3. Find the theoretical probability of choosing each pair of colors. Use probability notation. 4. Are all of the outcomes equally likely? Explain your reasoning. 5. How do the theoretical probabilities compare with your experimental probabilities? Explain any differences. 5
C. 1. Brelynn and Akimi change the rules of the game. Each contestant must predict which color combination will result from choosing a block from each bag. Brelynn and Akimi make the following predictions for this game. Akimi I predict 2 reds. Brelynn I predict 1 blue and 1 red, in either order. Who has the better chance of winning? Explain. 2. Does a contestant have a chance to win the bonus prize? Is it likely a contestant will win the bonus prize? Explain. 3. If you play this game 18 times, how many times do you expect to win? D. Melissa is designing a birthday card for her sister. She has a blue, a yellow, a pink, and a green sheet of paper. She also has a black, a red, and a purple marker. Suppose Melissa chooses one sheet of paper and one marker at random. 1. Make a tree diagram of all the possible color combinations. List all of the possible outcomes. 2. What is the probability that Melissa chooses pink paper and a red marker? Use probability notation. 3. What is the probability that Melissa chooses blue paper? Use probability notation. 4. What is the probability that she does not choose blue paper? Use probability notation. 5. What is the probability that she chooses a purple marker? Use probability notation. 6
WDYE 2.4: Homework Zaption 1. Lunch at school consist of a sandwich, a vegetable, and a fruit. Each lunch combination is equally likely to be given to a student. The students do not know what lunch they will get. Sol s favorite lunch is a chicken sandwich, carrots, and a banana. a. Make a tree diagram to determine how many different lunches are possible. List all the possible outcomes. b. How many different lunch combinations are there? c. What is the probability that Sol gets his favorite lunch? Explain your reasoning. d. What is the probability that Sol gets at least one of his favorite lunch items? Explain. 2. Suppose you spin the pointer of the spinner at right once and roll the number cube (the numbers on the cube are 1, 2, 3, 4, 5, and 6). a. Make a tree diagram of the possible outcomes of a spin of the pointer and a roll of the number cube. b. How many different combinations are there? c. What is the probability that you get a 2 on both the spinner and the number cube? d. What is the probability that you get a factor of 2 on both the spinner and the number cube? e. What is the probability that you get a multiple of 2 on both the number cube and the spinner? 7
Why was Jesse James in the Hospital? (E-51) Find each answer in the code at the bottom of the page. Write the letter of the problem above the answer each time it appears. Tree Diagram and List of Outcomes: Tree Diagram and List of Outcomes: Tree Diagram and List of Outcomes: Tree Diagram and List of Outcomes: 8
Tree Diagram and List of Outcomes: 9
Homework (E-49) 10
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