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.

   Hint (a):

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

   Partial answer (a):

   Bus $\#41$ MP3 Player
   Bus $\#41$ Letter
   Bus $\#41$ Book

2. Use your list to find the following probabilities:

   Hint (b):

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

   More Help (b):

   Find the numerator by counting from your systematic list.

   Partial Answer (b-ii):

   $\frac{8}{12}$

   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.

   Hint (c):

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