70B
Tree Diagrams
Tree Diagrams – are used to illustrate _______________________________________.
• A tree diagram is a graphical way to show all of the possible _______________________
in a situation or experiment.
Sample Space – is the __________ of all the __________________ in a probability experiment.
Let’s flip a coin.
Flip 1
Flip 2
Outcomes
Heads
Heads
HH
Tree Diagram
1. What is the probability of getting tails on both flips?
2. What is the probability of getting at least 1 tails?
Example 1:
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.
Tree Diagrams Practice
1) 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 to choose one crust with one topping.
How many outcomes are there?
2) How would your sample space change if you added bacon as a third topping choice? Draw the new tree
diagram.
How many outcomes are there?
Jane wants ice cream. The ice cream shop has the
above tree diagrams in the window to show
customers possible combination of ice cream they
sell.
3) How many total outcomes?
4) How many combinations would there be if the
ice cream shop added another flavor?
5) How many combinations can Jane get with
vanilla ice cream?
6) How many combinations can Jane get if the ice
shop runs out of nuts?
7) How many combinations can she get with
chocolate and strawberries?
Fundamental Counting Principle
Fundamental Counting Principle – uses ________________________ of the number of ways
each event in an experiment can occur to find the number of ______________________
outcomes in __________________________________.
Example 1:
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 Lengths
3
Petite
5
Regular
7
Tall
9
11
13
2. How many lengths are there?
15
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 Principle Practice
1) At Outback Steakhouse you can choose from 5 steaks cooked to your liking and have a choice of 3 different
sides as shown below.
New York Strip
Rare
Mashed Potatoes
Filet
Medium
Baked Potato
Ribeye
Well Done
Sweet Potato
Porterhouse
Sirloin
How many different steak dinners are possible?
2) Sally’s ice cream parlor has 5 types of ice cream, 3 kinds of cones and
4 different toppings. Which of the following shows the correct way to
find all of the possible combinations?
3) According to the table below, which expression is equivalent to the
total number of outfits made by 1 shirt, 1 pair of pants and 1 pair of
shoes?
Sale Items
Shirts
Pants
Shoes
Polos
Jeans
Sneakers
Tee
Khakis
Sandals
Long-sleeve
Sweat
Dress
5 + 3•4
5+3+4
5 • 12
5•3• 4
3+3+3
3 • (3 + 3)
32 + 3
3•3•3
4) The school soccer team is ordering new knee pads 5) Randall wants to buy a pizza. He can select from 5
for their uniforms. The knee pads come in 4
different sizes, 4 types of crust, and 12 toppings
different colors, 6 sizes, and 2 styles. How many
for his pizza. How many different outcomes of
different outcomes of knee pads are available?
pizzas can Randall order?
Fundamental Counting Principle Practice
Real Meal Restaurant
SANDWICHES:
Ham and Turkey Club
Rachael on Rye
Sliced BBQ
FRENCH FRIES:
Small
SALADS:
BEVERAGES:
Medium
Hamburger
Deli Cold Cut Special
Pork BLT
Large
Garden Salad
Chef Salad
Cobb Salad
Coke
Small
Pepsi
Small
Sprite
Small
Tea
Medium
Coffee
Medium
Milk
Regular
DRESSING:
Medium
Medium
Medium
Large
Large
Low-fat
Ranch
French
Italian
Large
Large
Large
6. Using the Fundamental Counting Principle, how many choices are there if a customer wants the
following meal options?
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?
Homework
Draw a tree diagram for each situation. Then verify the number of outcomes using the fundamental
counting principal.
1. For dessert you can choose apple, cherry, blueberry, or peach pie to eat and milk or juice to drink. How
many outcomes?
2. Show the outcomes for picking a vowel from the word APPLE and consonant from the word BOOK .
3. Judy tosses a coin 3 times. How many different outcomes are there?
4. John is taking a true/false quiz. There are 4 questions. How many outcomes?
Using only the fundamental counting principal, determine how many outcomes for each situation.
5. A store offers 3 brands of tee-shirts in 6 colors each in either long sleeve or short sleeve. How many
different shirts are there?
6. A dice is rolled 5 times. How many possible rolls are there?
7. A three-digit lottery ticket using the numbers 0 to 9 has how many possible combinations?