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 followingfruit flavors; strawberry, banana, or orange. How manydifferent choices of smoothies do you have?

EXAMPLE 1

Make a tree diagram to list all of the possible choices of smoothies.

STEP 1List the sizes.

STEP 2List the fruit choices for each size.

STEP 3List 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.

Refreshments1.

ANSWER

Practice – On Your Own

Course 2 TextbookPage 641 #8 Inflatable

Chairs # 9

EXAMPLE 2 Standardized Test Practice

EXAMPLE 2 Standardized Test PracticeEXAMPLE 2

SOLUTIONBecause 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

ANSWER The possible group assignments areRB, RY, GR, GB, GY, BR, BG, BY, YR, YG, and YB. The correct answer is C.

RG,

A B C 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?

Fruit2.

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?

Scheduling3.

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.

On Your Own

Course 2 TextbookPage 643 # 7 School

Lunch Page 644 #11 Muffins

EXAMPLE 3 Using a Tree Diagram

Find the probability of getting at least 2 heads whentossing 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; 112

ANSWER

On Your Own

Textbook Course 2page 641 # 3, 4, 5, 6

Spinners