1. Tree Diagrams Monday, October 15, 2012 Mr. Pearson
Probability
Tree Diagrams
Monday, October 15, 2012
Mr. Pearson

2. What are Tree Diagrams?
A way of showing the possibilities of two or more events
Simple diagram we use to calculate the probabilities of two or more events
Tree diagrams show you the outcomes that are possible while the Fundamental Counting Principle only tells you how many are possible, not the actual outcomes.

3. Using the fundamental counting principle we can figure out how many ways to order a pizza. Suppose your favorite pizza place had a special for a 1-topping pizza with the following options:
Size
Crust
Topping
                                      
small medium large
thin thick
cheese sausage pepperoni combo
Because the size, type of crust, and topping are all independent events, we can use the fundamental counting principle to determine how many different choices of pizza we could make.
number of pizzas = 3 sizes  • 2 crusts • 4 toppings = 3 • 2 • 4 = 24 possibilities

4. For example – a fair coin is spun twice
1st
2nd H HH
Possible Outcomes H T HT H TH T T TT

5. Tree Diagrams Shows all possible outcomes
Total amount of choices from a group of items
How many of a particular item out of all the possible choices

6. PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue
First write a list down the paper of the first item, in this case 1 to 5 1 2 3 4 5

7. PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue
Now determine how many options there are for the second item
There are 3 options:
Red
White
Blue

8. PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue
Draw “branches” off of each number. One for each second item, in this case 3. 1 2 3 4 5

9. PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue
At the end of each branch, write one of the three options from the 2nd items given. 1 2 3 4 5 R W B R W B R W B R W B R W B

10. PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue
Go to the last column of the tree diagram and count how many options are listed. 1 2 3 4 5 R W B R W B R W B R W B R W B

11. PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue
There are a total of 15 total choices listed

12. PROBLEM: What is the chance of choosing the color red?
There are five different times the color red could be chosen from all 15 options
The chance of having the color red is 5/15 or reduced is 1/3

13. Your turn! Please do on your own paper.
1. Give the total number of outcomes of choosing a hamburger, hot dog, or chicken and potato salad, coleslaw, or beans. Use a tree diagram.
2. What is the chance of having a hot dog? Write in fraction form.

14. PROBLEM: 1.Give the total number of outcomes of choosing a hamburger, hot dog, or chicken and potato salad, coleslaw, or beans. Use a tree diagram.
Answer:
Hamburger
Hot dog
Chicken
potato salad
coleslaw
beans
potato salad
coleslaw
beans
potato salad
coleslaw
beans

15. The answer is 3/9 and then simplified is 1/3
PROBLEM: 2. What is the chance of having a hot dog? Write in fraction form.
Answer:
First find out how many total options there are. Here there are a total of nine choices. This is your denominator.
Next find out how many options have a hot dog. Here there are a total of three choices. This is your numerator.
Finally, put the fraction in simplest form.
The answer is 3/9 and then simplified is 1/3
STOP