Lesson 5.2.4 – Teacher Notes Standard: 7.SP.C.8b Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 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. Full mastery of the standard can be expected by the end of the chapter. Lesson Focus: This lesson begins to summarize the work we did in prior lessons. Students will need to create sample spaces to answer questions. Emphasis is on lists. (5-56 and 5-58) I can identify the outcomes in sample space for an everyday event. Calculator: Yes Literacy/Teaching Strategy: Traveling Salesman (5-56 part e)

Bell Work

As you may have noticed in Lesson 5. 2 As you may have noticed in Lesson 5.2.3, considering probabilities with more than one event and more than two possibilities for each event (such as with the rock-paper-scissors game) can make keeping track of all of outcomes a challenge.  In this lesson, you will learn about probability tables, a new strategy for organizing all of the possibilities in a complicated game. Probability tables - An area model or diagram is one way to represent the probabilities of the outcomes for a sequence of two events.

5-54. TEN Os In this game, you will create a strategy to play a board game based on your predictions of likely outcomes.  You will place ten O’s on a number line.  Then your teacher will roll two number cubes  and add the resulting numbers.  As your teacher rolls the number cubes and calls out each sum, you will cross out an O over the number called.  The goal of the game is to be the first person to cross out all ten of your O’s. Talk with your team about the possible outcomes of this game.  Then draw a number line like the one below on your own paper.  Place a total of ten O’s on your number line.  Each O should be placed above a number.  You should distribute them based on what results you think your teacher will get.  More than one O can be placed above a number. 

5-55. Gerald’s strategy for the Ten O’s game was to place an O on each number from 1 to 10.  He was frustrated that his strategy of placing his ten O’s was not working, so he decided to analyze the game.  Gerald began by trying to create a table to list all of the possible combinations of rolls.  He made the table at right. Did he list them all?  If so, how can you be sure that they are all there?  If not, give examples of a few that he has missed. 

5-56.  Gerald decided that this method was taking too long, that it was too confusing, and that he made too many mistakes.  Even if he listed all of the combinations correctly, he still had to find the sums and then find the theoretical probabilities for each one.  Inspired by multiplication tables, he decided to try to make sense of the problem by organizing the possibilities in a probability table like the one shown below:

5-56 cont. a. How does Gerald’s table represent the two events in this situation?  What should go in each of the empty cells?  Discuss this with your team and then complete Gerald’s table on your own paper. b. How many total possible number combinations are there for rolling the two cubes?  Is each combination listed equally likely?  That is, is the probability of getting two 1’s the same as that of getting two 2’s or a 3 and a 1?  c. How many ways are there to get each sum?  Are there any numbers on the game board that are not possible to achieve?  d. What is the theoretical probability for getting each sum listed on the Ten O’s game board?  e. Now work with your team to determine a better strategy for Gerald to place his ten O’s on the game board that you think will help him to win this game.  Explain your strategy and your reasoning. 

5-58. Now go back and analyze the game of rock‑paper-scissors using a probability table to determine the possible outcomes. a. Make a probability table and use it to find the probability of Player A’s winning and the probability of Player B’s winning.  Did you get the same answers as before?  b. Do the probabilities for Player A’s winning and Player B’s winning add up to 1 (or 100%)?  If not, why not? 

Probability Tables The Scenario: You go to a birthday party. You have your choice of pizza (pepperoni, cheese, or sausage) and you have your choice of drink (Coke, Dr. Pepper, or Sprite). Your Task: Complete the Probability Table using the information you were given to show possible combinations of choices.   Pepperoni (P) Sausage (S) Cheese (C) Dr. Pepper (DP) Sprite (Sp) Coke (Ck) What’s the maximum number of events that you can have in a Probability table? Why?

Probability Tables Based on the Probability Table you just completed. Answer the following questions. 1) What is the probability of getting a Coke or Sprite and a cheese pizza? 2) What is the probability of getting any pizza with a Dr. Pepper? 3) What is the probability of getting Sausage pizza and a Coke?

Probability Tables The Scenario: You are attending a wedding. You have two choices for dinner (fish or chicken). You have four options for side dishes (mashed potatoes, Baked Potato, Rice, or Pasta. Your Task: Complete the probability Table with the information you were given and determine possible outcomes.  

Probability Tables Based on the Probability Table you just completed. Answer the following questions. 1) What is the probability of getting fish with rice? 2) What is the probability of getting chicken with any side? 3) What is the probability of getting rice with any meat?

Probability Tables The Scenario: You are attending a backyard cookout. You have four options for your meal. You have the choice of Hamburger, Hot Dog, Veggie Burger, or Sausage Dog. Along with your choice of meal, you have your choice of condiments and toppings (ketchup, mayonnaise, mustard, chili, or relish. Your Task: Draw a Probability Table to fit this scenario and identify the possible outcomes. Questions: What is the probability of having relish on any grilled food? What is the probability of having a hot dog with any condiment? What is the probability of having a burger with ketchup, mayonnaise, or mustard?

Determine how many outcomes you will have in each situation. How many different outcomes can you make if you have a spinner with 5 different colors and are rolling a 6 sided dice? 2. How many outcomes would you have if you had numbers 1 to 5 on separate cards in a bucket and seven students names in a hat to pick from? How many outfits can you make if you have a green, a red, a white, and a yellow shirt to wear with a pair of either blue, a black , or Khaki pants? You can have a sugar cookie, oatmeal cookie, or butter cookie with either icing, sprinkles, or frosting on top. How many different combinations can you make?