a The probability of selecting one bus and doing one activity is the product of their respective probabilities.
B
b Assume that each option of rides is equally likely, as are the four activities he can do while on his way home.
A
aDiagram:
Probability of Not Reading: 23
B
bDiagram:
Probability of Listening to MP3: 1/4
Practice makes perfect
a We are given a tree diagram and asked to complete it. Let's first add the last bus, #81, to the tree diagram.
To complete the diagram, we will also add the branches for each activity to the branches of #28, #55 and #81.
To calculate the probability of not reading, we can first determine the probability that she does read on the way home, and then find the complement of this.
1-P(read)
Let's mark all of the paths where she reads. It is equally likely she takes any of the buses, which means the probability of selecting a specific one of them is 14. Also, the chance of doing an activity on the bus is equally likely as well, and therefore the probability of doing one is 13.
To calculate the probability of selecting each of the highlighted branches, we have to multiply the probabilities along the path.
P(#41, read): 1/4* 1/3=1/12 [1em]
P(#28, read): 1/4* 1/3=1/12 [1em]
P(#55, read): 1/4* 1/3=1/12 [1em]
P(#81, read): 1/4* 1/3=1/12
To calculate the probability that Renae reads on her way home, we have to add all of the calculated probabilities.
P(reads): 1/12+1/12+1/12+1/12=4/12
Finally, we will calculate the complement of this to obtain the probability of her not reading.
b Greg has two choices of how to get home. He can go by bus, or by catching a ride with his brother.
While going home, Greg can do one of four things: listen to his MP3 player, play video games, read his novel for English, or talk to someone. Let's add these activities to the branches.
Let's mark all of the paths where he uses his MP3 player. We will assume that it is equally likely that he takes the bus or hitches a ride with his brother. Therefore, the probability of either option is 12. Also, the activities on the way home are equally likely and therefore, the probability of selecting one is 14.
To calculate the probability of selecting each of the highlighted branches, we have to multiply their respective probabilities.
P(#101, listen): 1/2* 1/4=1/8 [1em]
P(ride, listen): 1/2* 1/4=1/8 [1em]
Finally, we will add the calculated probabilities.
P(listens): 1/8+1/8=2/8
The probability of Greg listening to his MP3 player is 28, which can be reduced to 14.
