### Home > CCG > Chapter 3 > Lesson 3.2.2 > Problem3-67

3-67.

Recall from problem 3-56 that Renae can take one of four buses to get home: $\#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.

Creating a tree diagram, like the one started at right, is one way to organize all the outcomes of a sample space. This structure organizes the list by connecting each bus with each activity.

In this tree, the first set of branches represents the bus options. At the end of each of these branches are branches representing the activities. For example, if you follow the bold branches, Renae will take the #41 bus and will listen to her MP3 player.

1. On your paper, complete this tree diagram to show all of the different travel options that Renae could take. What is the probability that Renae does not read on the way home?

It may help to think of the problem like this: what is the probability that Renae writes or listens on the way home?

Is it easier to use the tree diagram shown above, or the one at right?

1. Renae’s cousin, Greg, can get home using the $\#101$ bus or by going with his older brother. On the way home, Greg can listen to his MP3 player, play video games on his MP3 player, read his novel for English, or talk to the person next to him. Make a tree diagram for all the possible outcomes. What is the probability Greg uses his MP3 player?

Remember that Greg uses his MP3 player for two of the four activities.