Build a Tree Diagram
Jason takes the car to school two days a week and the other days he rides his bike. If he has the car, the chance that he is late is 10%, but if he rides his bike it is 30%.
Use the materials given to your group to build a tree diagram to represent this problem.
1.
2.
Use your tree diagram to find the probability that on a randomly selected day Jason was:
b)
a)
Riding his bike and not late
c)
Driving his car given that fact that he was late
Late
1
Car
Bike
Late
LateC
Late
LateC
Start
0.4
0.6
0.1
Car
Bike
Late
LateC
Late
LateC
0.9
0.3
0.7
0.9
0.3
0.7
Start
0.4
0.6
0.1
2
Carl is not having much luck lately. His car will start only 80% of the time and his motorcycle starts only 60% of the time. a) Copy the tree diagram and record the probabilities for each branch.
M
C
Mc
Cc
M
Mc
b) Find the probability of each of the following outcomes:
c)
i) P(both will start)
ii) P(Carl has no choice but to use his car)
iii) P(Cc and M) iv) P(Cc and Mc)
Find the probability that Carl's motorcycle will start.
3
Conditional Probability with Tree Diagrams
A bag is randomly selected by spinning the spinner shown. Then a ticket is randomly selected from the appropriate bag.
Create a tree diagram.
Use the tree diagram to determine the probability that:
a) the ticket is red
b) the ticket was chosen from B given it is red
4
Of those students playing musical instruments, 60% were female. 20% of the females and 30% of the males play the violin.
a) Create a tree diagram.
b) What is the probability that a randomly selected student is male and does not play the violin?
c) What is the probability that a randomly selected student plays the violin?
d)
If a student plays the violin, what is the probability they are female?
5