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Home > GC > Chapter 4 > Lesson 4.2.1 > Problem 4-51


When a list is created by following a system (an orderly process), it is called a systematic list. Using a systematic list to answer questions involving probability can help you determine all of the possible outcomes. There are different strategies that may help you make a systematic list, but what is most important is that you methodically follow your system until it is complete. For the problem below, create a systematic list. Be prepared to share your strategy.

To get home, Renae can take one of four buses: , or . Once she is on a bus, she will randomly select one of the following equally likely activities: listening to her MP3 player, writing a letter, or reading a book.

  1. List all the possible ways Renae can get home. Use a systematic list to make sure you find all the combinations of a bus and an activity.

    Write the possibilities in an organized way so that you don't skip any.

    Bus  MP3 Player
    Bus  Letter
    Bus  Book

  2. Use your list to find the following probabilities:

    Find the numerator by counting from your systematic list.

    1. P(Renae takes an odd-numbered bus)

    2. P(Renae does not write a letter)

    3. P(Renae catches the # bus and then reads a book)

  3. Does her activity depend on which bus she takes? Explain why or why not.

    Look at your list. Do the possible activities change depending on which bus she takes.