### Home > GC > Chapter 4 > Lesson 4.2.1 > Problem4-51

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: $\#41$$\#28$$\#55$, or $\#81$. 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 $\#41$ MP3 Player
Bus $\#41$ Letter
Bus $\#41$ Book

2. Use your list to find the following probabilities:

$\text{Probability }=\frac{\text{number of desired outcomes}}{\text{number of possible outcomes}}$

Find the numerator by counting from your systematic list.

$\frac{8}{12}$

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

2. P(Renae does not write a letter)

3. P(Renae catches the #$28$ 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.