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4-22.

Joan and Jim are planning a dinner menu including a main dish and dessert. They have $4$ main dish choices (steak, vegetable-cheese casserole, turkey burgers, and vegetarian lasagna) and $3$ dessert choices (chocolate brownies, strawberry ice cream, and chocolate chip cookies).

1. Joan and Jim would like to know how many different dinner menus they have to choose from. One way to make sure you have considered the entire sample space – all the possible menu outcomes – is to make a table like the one at right. How many different menus are there?

 steak vegetable casserole turkey burgers vegetable lasagna chocolate brownies strawberry ice cream chocolate chip cookies

Each line represents one unique dinner menu.

Steak with Chocolate Brownies
Steak with Strawberry Ice Cream
Steak with Chocolate Chip Cookies

Vegetable Casserole with Chocolate Brownies
Vegetable Casserole with Strawberry Ice Cream
Vegetable Casserole with Chocolate Chip Cookies

Turkey Burgers with Chocolate Brownies
Turkey Burgers with Strawberry Ice Cream
Turkey Burgers with Chocolate Chip Cookies

Vegetable Lasagna with Chocolate Brownies
Vegetable Lasagna with Strawberry Ice Cream
Vegetable Lasagna with Chocolate Chip Cookies

$\left(4\ \text{main dish choices}\right)\left(3\ \text{dessert choices}\right)=12\ \text{menus}$

2. Assume the main dish choice and the dessert choice are both chosen randomly. Are all the menus equally likely?

3. What is the probability they pick a menu without meat? What is the probability they pick a menu with chocolate?