Course 2
Tree Diagrams and The Fundamental Counting Principle
*Tree Diagrams – are used to illustrate _______________________________________.
*A tree diagram is a graphical way to show _______________________________ in a situation
or experiment.
Sample Space – all of the _________________________ in a probability experiment.
Let’s flip a coin.
Flip 1
Flip 2
Outcomes
________
________
__________
________
________
__________
________
________
__________
________
________
__________
Tree Diagram
1. What is the probability of getting tails on both flips?
2. What is the probability of getting at least 1 tails?
3. A family has two children. Draw a tree diagram to show the sample space of the
children’s genders. Then determine the probability of the family having two girls.
You are trying to decide which pizza to order for dinner. Your choices for crust are: regular,
thin, and deep dish. You want only one topping and will choose either pepperoni or sausage.
Construct a tree diagram to show the possibilities you have from which to choose one crust with
one topping.
How would your sample space change if you added bacon as a third topping choice? Draw the
new tree diagram.
The Fundamental Counting Principal
The Jean Factory sells juniors’ jeans in different sizes and lengths.
The table shows what they have available.
1. According to the table, how many different sizes of juniors’
jeans are there?
Sizes
3
5
7
9
11
13
15
Lengths
Petite
Regular
Tall
2. How many lengths are there?
3. Find the product of the two numbers you found in questions 1 and 2.
4. Draw a tree diagram to help you find the number of different size and
length combinations. How does the number of outcomes compare to the
product you found above?
Fundamental Counting Principal: Uses multiplication of the number of
ways each even in an experiment can occur to find the number of possible
outcomes in a sample space.
1. Outback Steakhouse
 New York Strip
 Filet
 Ribeye
 Porterhouse
 Sirloin
- rare
- medium
- well done
How many different steak dinners are possible?
- mashed potatoes
-baked potatoes
-sweet potatoes
Course 2 Activity
Name __________________________
Tree Diagrams and the Fundamental Counting Principle
Directions:
* You are the new owner of a restaurant.
* As the owner, you must give your restaurant a name and create a menu for the restaurant.
* Your menu must include the following:
1) The name of your restaurant
2) The owner’s name (your name)
3) At least 3 main course items (i.e. – hamburger, pizza, etc)
4) At least 4 side items (i.e. – French fries, vegetables, salad, etc.)
5) At least 2 desserts
6) At least 2 drinks
7) At least 2 pictures
* You may type your menu or write it neatly on a piece of computer paper.
* Once you have completed your menu, write 3 questions about your menu.
* All questions should involve probability. At least 1 question must use a tree diagram and at
least 1 question must use the fundamental counting principle.
* Your questions may be typed or written neatly on a piece of computer paper.
* You must include an answer key.
* This will be a quiz grade. It will be graded for accuracy as well as completion and neatness.
Grading Rubric
Requirement
Point Value
Restaurant Name
5 points
Owner’s Name
5 points
3 Main Course Items
10 points
4 Side Items
10 points
2 desserts
10 points
2 drinks
10 points
2 pictures
10 points
3 questions
15 points
Answer Key
15 points
Neatness
10 points
Total Points
100 points
Points Earned
Course 2 Homework
Tree Diagrams & the Fundamental Counting Principle
Name ______________
Real Meal Restaurant
SANDWICHES:
Ham and Turkey Club
Rachael on Rye
Sliced BBQ
FRENCH FRIES:
small
SALADS:
Garden Salad
Chef Salad
Cobb Salad
medium
Hamburger
Deli Cold Cut Special
Pork BLT
large
DRESSINGS:
Ranch
French
Creamy Italian
BEVERAGES:
Coke
small medium
large
Pepsi small
medium large
Sprite small
medium large
Tea:
medium large
Coffee: medium large
Milk:
regular low-fat
1. How many choices are there if a customer wants the following: Display the choices with a
Tree Diagram. Then verify your answer using the Fundamental Counting Principle. Use the
back if needed.
a.
A soft drink, sandwich and fries?
b.
A sandwich, fries and milk?
c.
A salad with dressing and tea?
d.
A sandwich, salad with dressing, and coffee?