Bell WorkThree-course dinners can be made from the menu shown. Find the sample space for a dinner consisting of an appetizer, entrée, and dessert.

Hint: Draw a tree diagram

Bell Work

Soup

Salad

ChickenFish

Steak

ChickenFish

Steak

Apple PieCarrot Cake

Apple PieCarrot Cake

Apple PieCarrot Cake

Apple PieCarrot Cake

Apple PieCarrot Cake

Apple PieCarrot Cake

Sample SpaceSoup, Steak, Carrot CakeSoup, Steak, Apple Pie

Soup, Chicken, Carrot CakeSoup, Chicken, Apple Pie

Soup, Fish, Carrot CakeSoup, Fish, Apple Pie

Salad, Steak, Carrot CakeSalad, Steak, Apple PieSalad, Chicken, Carrot CakeSalad, Chicken, Apple PieSalad, Fish, Carrot CakeSalad, Fish, Apple Pie

Counting Outcomes

Counting Outcomes The Fundamental Counting Principle allows you to calculate the number of possible outcomes without creating a tree diagram and counting the possible outcomes in the sample space.

Counting Outcomes

Counting Outcomes

Let’s look back at the bell work…Sample Space

Soup, Steak, Carrot Cake Salad, Steak, Carrot CakeSoup, Steak, Apple Pie Salad, Steak, Apple PieSoup, Chicken, Carrot Cake Salad, Chicken, Carrot CakeSoup, Chicken, Apple Pie Salad, Chicken, Apple PieSoup, Fish, Carrot Cake Salad, Fish, Carrot CakeSoup, Fish, Apple Pie Soup, Fish, Apple Pie

How many options did you find when you did the tree diagram?

12

Let’s use the fundamental counting principle.

2 x 3 x 2 = 12

Counting Outcomes

✔Check Your ProgressFind the total number of outcomes when choosing from bike helmets that come in three colors and two styles.

6

✔Check Your ProgressIf the Jeans Shop adds relaxed fit jeans to its selection, find the number of available jeans. Then find the probability of randomly selecting a 36 x 30 relaxed fit pair of jeans. Is it likely or unlikely that the size would be chosen?

60; 1/60;

unlikely

✔Check Your UnderstandingRally Coach

4 x 3 = 12

20 x 7 = 140

12 x 7 = 84

3 x 4 = 12 6 x 2 x 2 =

24

4 x 2 x 2 = 16