Lesson 5.2.6 Day 1 – Teacher Notes Standard: 7.SP.C.8a and b 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. 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: The focus of today is finding probability using tables, (rectangular models). (5-78) I can choose the appropriate method such as organized lists, tables, and tree diagrams to represent sample spaces for compound events. Calculator: Yes Literacy/Teaching Strategy: Reciprocal Teaching (Intro); Hot Potato (5-78)

Bell Work

Day 1 In Lesson 5.2.5, you used systematic lists, probability tables, and probability trees to organize the outcomes of different probability situations.  Today you will use a probability table to help organize events when one outcome is more likely than another.

5-76. Nina is buying a new pet fish 5-76. Nina is buying a new pet fish.  At the pet store, the fish tank has an equal number of two kinds of fish: tetras and guppies.  Each kind of fish comes in four different colors: yellow, orange, blue, and silver.  There are an equal number of each color of fish in the tank. a. If Nina scoops out a fish at random, what is the probability that she will scoop out a silver tetra?  Show how you decided. 

5-76 cont. b. Nina set up the table below, to organize the different possible outcomes.  She represented the kind of fish on one side of her table and the color possibilities on the other.  What do the fractions inside her table represent?  c. As Nina looked at her work, she noticed that her table looked a lot like a rectangle with the area divided into parts.  “Could that help me calculate the probabilities?” she wondered.  She used the length and width of the silver tetra section to set up this equation: 1 4  1 2 = 1 8 . How does this equation relate to the length, width, and area of this section of the rectangle?  Does this match the probability you found in part (a)?  d. What is the area of the complete large rectangle? 

5-77. TESTING THE AREA MODEL Nina decided to see if thinking about finding area would help find other probabilities.  She put three cubes in a bag: two blue cubes and one yellow cube.  She pulled one cube out, put it back in the bag, and then drew another. a. Use a systematic list or a probability tree to organize the possible color combinations she could draw.  How many are there?  What is P(blue and blue)?  b. This time, Nina made the table at right.  Based on the table, what is the probability of drawing two blue blocks?  Is this the same probability you found in part (a)? 

5-77 cont. c. Looking at her work, Edwin said, “I think I can simplify this diagram.”  His rectangle is shown at right.  What is the area of the section representing blue and blue?  Does this match the probability that Nina found?

5-78. The pet store sells a lot of pet food 5-78. The pet store sells a lot of pet food.  On a slow day at the pet store, three people buy cat food, two people buy dog food, and one person buys food for a pet snake.  If half of the customers pay with cash and half pay with credit card, what is the probability that a customer buying pet food will buy dog food with cash?  Set up an area model like Edwin’s in part (c) of problem 5‑77 to help you find the probability. 

There are three yes cards in the bag with 2 maybe cards. How many opportunities can you get yes first and then maybe with replacement? Make sure kids understand what each side of the table represents (left side as first event, top side as the 2nd event.

You can either get an Android or iPhone . The phone come in these three colors. You can either choose gold, pale blue, dark blue and grey. What is the chance of getting an iPhone that is blue or grey? What is the chance of getting a gold phone? What is the probability of getting an Android that is not blue?

Practice Find the area of these rectangles: b. b. c. d. e.