Download Unit 5 Chapter 9 Section 3 Sample Spaces.notebook

Unit 5 Chapter 9 Section 3 Sample Spaces.notebook
April 05, 2016
Unit 5 - Chapter 9 - Section 3
Sample Spaces
Objective: To make and use sample spaces and to use the counting principle
Sample Space: the collection of all possible outcomes
in an experiment
Tree Diagram: a way to show all the possible
outcomes in an experiment
Counting Principle: Suppose there are m ways of
making one choice and n waysof making a second choice.
Then there are m(n) ways to make the first choice
followed by the second choice.
Unit 5 Chapter 9 Section 3 Sample Spaces.notebook
April 05, 2016
Finding a Sample Space
1) Fill in the table to find the sample space for rolling two number cubes. Write the outcomes as ordered pairs.
a) Find the probability of rolling at least one 3.
b) Find the probability of rolling doubles.
c) Find the probability of rolling a sum of 6.
2) Fill in the table to find the sample space for tossing two coins. a) Find the probability of getting two heads.
b) Find the probability of getting a head and a tail.
Unit 5 Chapter 9 Section 3 Sample Spaces.notebook
April 05, 2016
Using a Tree Diagram
You can also show a sample space by using a tree diagram. Each branch of the tree represents one choice.
3) Suppose you are going to travel on a river. You have two choices of boats ­ a kayak or a rowboat. You can go upstream on three smaller streams, to the north, northwest, and northeast.
a) What is the sample space for your journey? Make a tree diagram for the possible outcomes.
b) Suppose you select a trip at random. What is the probability of selecting a kayak and going directly north?
c) Suppose a canoe is added as another choice of boats. Draw a tree diagram to show the new sample space.
d) Find the probability of selecting a canoe at random for the trip.
Unit 5 Chapter 9 Section 3 Sample Spaces.notebook
April 05, 2016
Using the Counting Principle
Sometimes it may be too tedious to make a sample space. At those times, you can use the Counting Principle to find the number of outcomes there are.
4) How many different sandwiches can you order when you choose one bread and one meat from the menu.
The Deli Sandwiches
Fresh Breads Deli Meats
Roast Beef
Rye
Turkey
Wheat
Ham
White
Pastrami
Pita
Salami
Wrap
Liverwurst
5) A manager at the Deli decides to add chicken to the list of meat choices. How many different sandwiches are now available?
Unit 5 Chapter 9 Section 3 Sample Spaces.notebook
April 05, 2016
Challenge
Refer to the number cube, spinner, and cards below. Using the Counting Principle, determine the number of outcomes, then find each probability. Blue
Red
Green
V W X
Y Z
1) You roll the die and spin the spinner. P(2, red)
2) You roll the die and pick a card. P(even #, Z)
3) You roll the die, spine the spinner and pick a card. P(number < 5, blue, not W)
Unit 5 Chapter 9 Section 3 Sample Spaces.notebook
April 05, 2016
Closure
Draw a tree diagram to show the sample space, then use the tree diagram to answer the following probability questions.
1) The number cube is rolled and the spinner is spun. Blue
Red
Green
a) P(2, blue)
b) P(1 or 3, green)
c) P(7, purple)
d) P(even #, red or blue)
Unit 5 Chapter 9 Section 3 Sample Spaces.notebook
Homework
Practice Worksheet 9­3
April 05, 2016