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)

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 event 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? 

Tree Diagrams Shows all possible outcomes….. Total amount of choices from a group of items How many of a particular item out of all the possible choices

First write a list of the first item, in this case 1 to 5 1 2 3 4 5 PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue First write a list of the first item, in this case 1 to 5 1 2 3 4 5

Now determine how many options there are for the second item PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue Now determine how many options there are for the second item There are ___ options:

PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue First write a list of the first item, in this case 1 to 5 1 2 3 4 5 #2 Draw “branches” off of each number. One for each second item (red, white, or blue), in this case 3. #3 At the end of each branch, write one of the three options from the 2nd items given.

PROBLEM: What is the chance of choosing the color red?

3.What is the probability of getting the number greater than 3? PROBLEM: 1. What is the chance of getting an even number and the color white? 2. What is the probability of getting a number less than 5 and either blue or red? 1 2 3 4 5 red white blue red white blue red white blue red white blue red white blue 1 red 5 red 1 white 1blue 2 red 3 red 4 blue 2 white 2 blue 3 white 3 blue 4 red 4 white 5 white 5 blue 3.What is the probability of getting the number greater than 3?

PROBLEM: 1.Find the total number of outcomes of choosing a hamburger, hot dog, or chicken and potato salad, coleslaw, or beans. Use a tree diagram. PROBLEM: 2. What is the chance of having a hot dog? Write in fraction form.

PROBLEM: Using the last scenario 2 PROBLEM: Using the last scenario 2. What is the probability of getting chicken with potato salad or beans? 3. What is the probability of getting any meat with coleslaw? 4. What is the probability of getting hotdog or hamburger? 5. What is the probability of getting any meat with just beans?

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. 

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.

You are getting a new phone for Christmas You are getting a new phone for Christmas. You can choose from either an IPhone X, Samsung Galaxy S9, or Google Pixel 2. Each phone comes in grey, sky blue, or pink. Make a probability tree to show how many different combinations you can have. (Show me your tree after you have it drawn)

1. How many combinations can you have? 2. What is the chance of you getting an Google Pixel 2 that is blue? 3. What is the probability of not getting an IPhone X that is grey?

If you go to the movies this weekend, you have a choice of seeing First Man, Goosebumps 2: Haunted Halloween, Small Foot, or Venom (3D). You can go at 2:30, 5:00, or 7:00. Make a probability tree that shows all of the options you can choose (what you are going to see and the time).

What is the probability of going to Venom at 7:00? What is the probability of going to Small Foot at either 2:30 or 5:00? What is the probability of seeing a movie at 7:00? What is the probability of seeing First Man, Small Foot, or Venom (3D) at 5:00 or 7:00?

Get a copy of the practice sheet, and begin working through it.