Tree Diagrams 70B - Loudoun County Public Schools

Tree Diagrams

70B

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

Heads

Flip 2 Heads

Outcomes 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?

2. How many lengths are there?

Sizes Lengths 3 Petite 5 Regular 7 Tall 9 11 13 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?

5+3?4 5 ?12

5+3+ 4 5?3? 4

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

3+3+3

32 + 3

3 ? (3 + 3)

3?3?3

4) The school soccer team is ordering new knee pads for their uniforms. The knee pads come in 4 different colors, 6 sizes, and 2 styles. How many different outcomes of knee pads are available?

5) Randall wants to buy a pizza. He can select from 5 different sizes, 4 types of crust, and 12 toppings for his pizza. How many different outcomes of pizzas can Randall order?

Fundamental Counting Principle Practice

Real Meal Restaurant SANDWICHES: FRENCH FRIES: SALADS:

BEVERAGES:

Ham and Turkey Club Rachael on Rye Sliced BBQ

Hamburger Deli Cold Cut Special Pork BLT

Small

Medium 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

Large Large Large

Ranch French Italian

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?

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