Lesson 5.2.5 – Teacher Notes Standard: 7.SP.C.8a Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 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. Full mastery of the standard can be expected by the end of the chapter. Lesson Focus: The focus of this lesson is for students to gain additional practice with compound probability. There is an emphasis on using tree diagrams to show possible outcomes. (5-68) I can recognize that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Calculator: Yes Literacy/Teaching Strategy: Reciprocal Teaching (Intro); Swapmeet (closure); Huddle (Student struggles)

Bell Work Create a table of all the possible probability outcomes in the following situation. Ty is going out to eat at the new Taco Shack in town. The Taco Shack has different options of meat: chicken, steak, tofu, or ground beef. It also has different choices of shells: soft shell, hard shell, or a burrito. Lastly, they had multiple different toppings to choose from: lettuce, Pico de gallo, sauce, peppers, or cheese. How many different option choices does Ty have at the new Taco Shack? Show ALL of your work.

In this lesson you will work with different models for organizing outcomes of multiple events when both one event and another event occur.  Throughout this lesson, use these questions to help focus your team’s discussion. Is there more than one event? Do both one event and other events occur? Are the events independent?

5-65. THE DOUBLE SPIN A giant wheel is divided into 5 equal sections labeled –2, –1, 0, 1, and 3.  At the Double Spin, players spin the wheel shown at right two times. The sum of their spins determines whether they win.      Work with your team to determine probabilities of different outcomes by answering the questions below: a. Make a list of the possible sums you could get.   

5-65 cont. b. Which sum do you think will be the most probable? c. Create a probability table that shows all possible outcomes for the two spins. d. If Tabitha could choose the winning sum for the Double Spin game, what sum would you advise her to choose?  What is the probability of her getting that sum with two spins?

5-66. Scott’s job at Crazy Creations Ice Cream Shop is to design new ice cream flavors.  The company has just received some new ingredients and Scott wants to be sure to try all of the possible combinations.  He needs to choose one item from each category to create the new flavor.  Base Flavor Chunky Mix-In Fruit Swirl Vanilla Hazelnuts Apricot Chocolate Sprinkles Plum Toffee Bits Berry Grape a. Without talking with your teammates, list three different combinations Scott could try.  Make sure you use the word “and.”  Then share your combinations with your study team.  How many different combinations did you find?  Do you think you found all of the possibilities? 

5-66 cont. b. Creating a list of all of the possibilities would take time and require a lot of writing the same words over and over.  Because there are more than two options, a probability table is also challenging.  An alternative is creating a probability tree to show the different combinations.  A probability tree, like the one started on the Lesson 5.2.5 Resource Page, shows the different possibilities branching off each other.  In this case, the two segments on the left show the base flavors.  Each different mix-in choice branches off of the base flavor, and each fruit swirl branches off each mix-in choice.  The first letter of each choice is used to label this diagram. The bold line in the diagram shows the combination vanilla, toffee bits and plum swirl.  Complete the probability tree to show all of the possible combinations. 

Mutually Exclusive Event: two events are said to be mutually exclusive if they have no outcome in common 5-66 cont. c. How many different flavor combinations are possible?  Where do you look on the diagram to count the number of complete combinations?  d. Use your probability tree to help you find the probability that Scott’s final combination will include plum swirl. e. What is the probability that his final combination will include hazelnuts? 

5-68. In a power outage, Rona has to reach into her closet in the dark to get dressed.  She is going to find one shirt and one pair of pants.  She has three different pairs of pants hanging there: one black, one brown, and one plaid.  She also has two different shirts: one white and one polka dot. a. Draw a probability tree to organize the different outfit combinations Rona might choose.  b. What is the probability that she will wear both a polka dot shirt and plaid pants?    

5-68 cont. c. What is the probability that she will not wear the black pants?   d. For what kinds of problems can you also make a probability table?  If it is possible, make a probability table for Rona’s outfits.  Which way of representing the outcomes do you like better?   e. Are the events polka dot and plaid mutually exclusive?  Explain. f. Are the events polka dot and white mutually exclusive?  Explain.

Get a copy of the practice sheet, and begin working through it. Wendy has the following choices when walking through the lunch line: Chocolate ice cream Vanilla ice cream Swirl ice cream Her choices of toppings are: Chocolate chips Sprinkles Caramel Drizzle Her choice of cones are: Waffle cone Sugar Cone Paper bowl Draw a probability tree P(outcome with caramel drizzle): P(NOT sugar cone): P(Chocolate AND drizzle): Name an example of a mutually exclusive event: Name an example of a NOT mutually exclusive event:

Homework Pages: Page 138 Pages 257-258 Pages 278-279