1. Finding Probability Using Tree Diagrams and Outcome Tables

2. Tree Diagrams
If you flip a coin twice, you can model the possible outcomes using a tree diagram or an outcome table
Tree Diagram: Outcome table: H T
Flip 1
Flip 2
Simple
Event H HH T HT TH TT T

3. Tree Diagrams
if you rolled 1 die and then flipped a coin you have 12 possible outcomes H T
(1,H) 1
(1,T) H T
(2,H) 2
(2,T) H T
(3,H) 3
(3,T)
(4,H) H T 4
(4,T) H T
(5,H) 5
(5,T)
(6,H) H T 6
(6,T)

4. Multiplicative Principle for Counting
How many possible 3-letter words are there?
There are 26 possibilities for the first letter
There are 26 possibilities for the second letter
There are 26 possibilities for the third letter
Total possibilities = 26 x 26 x 26 = 17576
How many possible postal codes are there in Canada?
Total possibilities = 26 x 10 x 26 x 10 x 26 x 10 =

5. Calculating probabilities of independent events
You roll a die and flip a coin
Are they independent or dependent on each other?
To get the probability of two independent events occurring, simply multiply the probability of each individual event together
P(odd, head) = P(odd) x P(head)
= ½ x ½
= ¼

6. Example 1: tree diagram
a sock drawer has a red, a green and a blue sock
you pull out one sock, replace it and pull another out
a) draw a tree diagram representing the possible outcomes
b) what is the probability of drawing 2 red socks?
these are independent events R B G

7. Example 2
a) If you draw a card, replace it and draw another, what is the probability of getting two aces?
These are independent events
4/52 x 4/52
b) If you draw an ace and then draw a second card (“without replacement”), what is the probability of two aces?
second event depends on first event
4/52 x 3/51

8. Example 3 - Predicting Outcomes
Mr. Xu is playing Texas Hold’Em
He finds that he wins 70% of the pots when he does not bluff
He also finds that he wins 50% of the pots when he does bluff
If there is a 60% chance that Mr. Xu will bluff on his next hand, what are his chances of winning the pot?
We will start by creating a tree diagram

9. Win pot
P=0.6 x 0.5 = 0.3
0.5
bluff
0.6
0.5
Lose pot
P=0.6 x 0.5 = 0.3
Win pot
0.7
P=0.4 x 0.7 = 0.28
0.4
no bluff
0.3
Lose pot
P=0.4 x 0.3 = 0.12

10. Homework Read the examples on pages 239-244
Try pp. 245 – 249 #2, 3, 5, 7, 9, 12, 13a, 14