Name _______________________________________
Lesson 1.2 – Compound Probability
Period ____
Math 7ACC
Essential Vocabulary
Compound Event: an event that consists of two or more simple events
Compound Probability: the probability of a compound event
Fundamental Counting Principle: multiplying all possible outcomes per event in a compound event gives
you the total number of possible outcomes
Sample space: a list of possible outcomes for one or more events
We can find the sample space by using:
◼ A grid/table (can be used when you have exactly 2 events)
◼ A tree diagram (can be used with any number of events)
◼ Sometimes you can make a list from memory … but be careful not to forget or repeat!
Example A: Rolling Two Number Cubes
Charlotte is playing a board game that requires her to roll two number cubes at the same time. Use a model to list
the sample space of all possible outcomes.
Before we make a model, we can use the Fundamental Counting Principle to determine the total number of
possible outcomes.
Fundamental Counting Principle
Simple Event #1 (rolling a number cube): __________ possible outcomes
______ × ______ = ______ total
Simple Event #2 (rolling a number cube): __________ possible outcomes
possible outcomes
Use the models to help you answer the following questions.
How many outcomes
have the same number
on both dice?
How many outcomes
How many outcomes
have two even numbers? have a sum of at least
10?
How many total
outcomes are there?
Use the models to help you find the following probabilities.
P(odd, even)
P(sum > 12)
P(first # < second #)
P(5, 5)
Example B: Playing Rock, Paper, Scissors
Reese and James are playing rock, paper, scissors. What is the probability that at least one person will show rock? (Assume all
outcomes are equally likely.)
Before we make a model to help us answer the question, we can use the Fundamental Counting Principle to determine the
total number of possible outcomes.
Fundamental Counting Principle
Simple Event #1 (James’ choice): __________ possible outcomes
Simple Event #2 (Reese’s choice): __________ possible outcomes
______ × ______ = ______ total
possible outcomes
Sample Space
How many possible outcomes are in the sample space?
Explain the difference between PR and RP.
List all the ways that at least one rock comes up. How
many are there?
What is the probability of at least 1 rock coming up?
Example C: More Than Two Simple Events
At a smoothie stand, you can order a fruit smoothie in three different sizes: small,
medium, or large. You can choose strawberries, mango, or both fruits. Then, you can
choose to add yogurt or not. If all types of smoothies are equally likely to be ordered,
what is the probability that someone will order a smoothie with strawberries and
yogurt in it?
Since we are not asked
for sample space, we
do not have to list ALL
outcomes here …
List all FAVORABLE outcomes
(that include strawberries & yogurt)
How many total outcomes are in the sample space?
For each size, how many smoothies have both
strawberries and yogurt?
What is the probability of ordering a smoothie with
strawberries and yogurt?
What is the probability of an order not being a
smoothie with strawberries and yogurt?
Example D: Making a Tree Diagram (3 events … with guides)
For a family picnic, Mr. Lucas set up a sandwich station with three choices of bread (wheat, Italian, or rye), two types of
meat (turkey or ham), and two types of cheese (American or cheddar). Each sandwich has exactly one of each type of
ingredient, and each ingredient is equally likely to be chosen. Make a tree diagram to show the sample space.
Bread
W = wheat
I = Italian
R = rye
Key
Sandwich
T = turkey
H = ham
Cheese
A = American
C = cheddar
How many possible outcomes should there be
when you finish your tree diagram?
Use the fundamental counting principle!
Sample Space
Use your tree diagram for Mr. Lucas’ sandwich station to answer the following questions:
A. How many total possible sandwich
combinations are there?
B. How many outcomes have ham?
C. How many outcomes have cheddar cheese
or ham?
D. How many outcomes have cheddar cheese
and ham?
E. How many outcomes do not have meat?
F. How many outcomes have cheese?
G. What is the probability that he will choose
a turkey sandwich?
H. What is the probability that he will choose a
sandwich with American cheese?
I.
J.
What is the probability that he will choose
a sandwich with turkey and American
cheese?
K. What is the probability that he will choose
a sandwich with cheese?
What is the probability that he will choose a
sandwich with rye bread?
L. What is the probability that he will choose a
sandwich with pumpernickel bread?
Example E: Making a Tree Diagram (2 events, without replacement)
Katie is playing a word game in which tiles with single letters on them are drawn from a bag. When each tile is removed,
it is placed to the side. Toward the end of the game, the remaining tiles have the letters N, A, C, H, O and S. Katie draws
two tiles at random. List the sample space of her possible outcomes.
Before we make a model to show the sample space, we can use the Fundamental Counting Principle to determine the
total number of possible outcomes.
Fundamental Counting Principle
Simple Event #1 (Picking a letter): __________ possible outcomes
Simple Event #2 (Picking a second letter): __________ possible outcomes
______ × ______ = ______ total
possible outcomes
Remember, she
cannot pick the
same tile twice!
Option 1: Make a Tree Diagram
You can also represent the sample space by using a tree diagram. The top letters are the first letter drawn. The lower
letters are the second letter drawn. Complete the diagram.
Option 2: Make a List
You can make a list that shows all of the possibilities. Each listed pair is (first draw, second draw). Be sure to use a pattern
to help you not skip any combinations!
Example F: Making a Tree Diagram (3 events … no guides)
Daren sells sweatshirts in small, medium, and large sizes. The sweatshirts are sold both with and without hoods, and they
are available in gray, red, and yellow.
A) How many outcomes are possible?
B) Draw a tree diagram to represent the sample space.
C) What is the probability that a randomly chosen sweatshirt is medium with a hood?
D) How many outcomes are small and yellow?
E) What is the probability that a randomly chosen sweatshirt is gray without a hood?