### Home > CCG > Chapter 3 > Lesson 3.2.1 > Problem3-56

3-56.

When you list all of the possible outcomes in a sample space by following an organized system (an orderly process), it is called a systematic list. 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.

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. Create the sample space of all the possible ways Renae can get home and do one activity by making a systematic list.

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 sample space 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?