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.

Sizes / Lengths
3
5
7
9
11
13
15 / Petite
Regular
Tall

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?

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 - rare - mashed potatoes

·  Filet - medium -baked potatoes

·  Ribeye - well done -sweet potatoes

·  Porterhouse

·  Sirloin

How many different steak dinners are possible?

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 / Points Earned
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

Course 2 Homework Name ______

Tree Diagrams & the Fundamental Counting Principle

Real Meal Restaurant

SANDWICHES: Ham and Turkey Club Hamburger

Rachael on Rye Deli Cold Cut Special

Sliced BBQ Pork BLT

FRENCH FRIES: small medium large

SALADS: Garden Salad DRESSINGS: Ranch

Chef Salad French

Cobb Salad 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?