Lesson 7 SP 7 Sample Space

EXAMPLE 1 Making a Tree Diagram Fruit Smoothies You are ordering a fruit smoothie. You can choose a small, medium or large smoothie in one of the following fruit flavors; strawberry, banana, or orange. How many different choices of smoothies do you have?

EXAMPLE 1 Make a tree diagram to list all of the possible choices of smoothies. STEP 1 List the sizes. STEP 2 List the fruit choices for each size. STEP 3 List the outcomes Making a Tree Diagram ANSWER There are 9 different choices of smoothies.

GUIDED PRACTICE for Example 1 Popcorn at a movie theater comes in regular, large, and jumbo sizes, and it comes either plain or buttered. How many choices of popcorn do you have? Make a tree diagram to solve the problem. Refreshments 1. ANSWER

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EXAMPLE 2 Standardized Test Practice

EXAMPLE 2 Standardized Test Practice EXAMPLE 2 SOLUTION Because you cannot be in the same group for both sessions, do not include the same group in both sessions in the tree diagram. First Second ANSWERThe possible group assignments are RB, RY, GR, GB, GY, BR, BG, BY, YR, YG, and YB. The correct answer is C. RG, ABC D Standardized Test Practice

GUIDED PRACTICE for Example 2 You have a plum, a banana, an apple, an orange, and a pear. If you eat one now with lunch and eat one later for a snack, what are all the possible pairs of fruit you can select for lunch and the snack? Fruit 2. ANSWER plum banana, plum apple, plum orange, plum pear, banana plum, banana apple, banana orange, banana pear, apple plum, apple banana, apple orange, apple pear, orange plum, orange banana, orange apple, orange pear, pear plum, pear banana, pear apple, pear orange

GUIDED PRACTICE You have 6 movies. You want to watch one now, and a different one later. How many ways can you choose two movies to watch? Scheduling 3. for Example 2 30 waysANSWER

GUIDED PRACTICE ANSWER If another color is added in the second session there will be another four groups in the list of possible group assignments, RR, BB, GG, and YY. ANSWER for Example 2 In Example 2, how would the diagram of possible outcomes change if you could be assigned to the same color group for both sessions? Explain. What If? 4.

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EXAMPLE 3 Using a Tree Diagram Find the probability of getting at least 2 heads when tossing a coin 3 times. Make a tree diagram to list the outcomes, or sample space, of the experiment. Circle the successful outcomes. First Second Third

EXAMPLE 3 ANSWER Because 4 of the 8 outcomes have at least 2 heads, the probability is 4 8, or 1 2 Using a Tree Diagram

GUIDED PRACTICE for Example 3 5. You roll a number cube and flip a coin. Make a list of possible outcomes. What is the probability that you get a 3 and tails? 1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T; 1 12 ANSWER

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