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Home > CCG > Chapter 4 > Lesson 4.1.2 > Problem 4-22

4-22.

Joan and Jim are planning a dinner menu including a main dish and dessert. They have main dish choices (steak, vegetable-cheese casserole, turkey burgers, and vegetarian lasagna) and 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

    Diagram with two columns, Main Dishes and Desserts. Under Main Dishes is Steak, Vegetable Casserole, Turkey Burgers, and Vegetable Lasagna, Under Desserts is Chocolate Brownies, Strawberry Ice Cream, and Chocolate Chip Cookies, An orange line is drawn from Steak to each of the 3 desserts, A blue line is drawn from Vegetable Casserole to each of the 3 desserts. A purple line is drawn from Turkey Burgers to each of the 3 desserts. A green line is drawn from Vegetable Lasagna to each of the 3 desserts.

    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

  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?