a Let's draw a tree diagram as described in the exercise.
b To determine probability, we have to divide the number of possible outcomes with the number of favorable outcomes.
P=Number of favorable outcomes/Number of possible outcomes
Let's determine the probabilities one at the time.
i. P(Renae Takes an Odd-Numbered Bus)
To determine this probability we are only concerned with the first set of branches as the activity is not important. Let's highlight the branches with odd-numbered buses.
Three of four buses are odd-numbered. Now we can determine the probability of Renae taking an odd-numbered bus.
P=3/4
ii. P(Renae Does Not Write A Letter)
We want to know the probability of not writing a letter. Therefore, let's highlight all the branches where Renae does not write a letter.
We have a total of twelve outcomes and for eight of these Renae does not write a letter. Now we can determine the probability of Renae not writing a letter.
P= 812=2/3
iii. P(Renae Catches The #28 Bus And Then Reads A Book)
We want to know the probability of first catching the #28 busy and then reading a book. Let's highlight this outcome.
We have a total of twelve outcomes and for one of these, Renae catches the #28 bus and then reads a book. Now we can determine the probability of this happening.
P= 112
iv. P(Renae Does Not Read On The Way Home)
We want to know the probability of Renae not reading on the way home. Therefore, let's highlight all the branches where Renae does not read on the way home.
We have a total of twelve outcomes and for eight of these, Renae does not read on her way home. Now we can determine the probability of Renae not reading on the way home.
P= 812=2/3
c No, the bus she steps onto does not influence the activity she chooses to do. These are called independent events, which means the probability of one event does not affect the probability of the other event.
