Counting Outcomes

1
Counting Outcomes

• Tree Diagrams are a visual diagram that shows the
  total number of possible outcomes.
• Ex. 1 You have three shirts a t-shirt, a
  hoodie, and a sweater. You also have two pairs
  of pants blue jeans and khaki slacks.
  How many different outfits can you wear?
• Lets draw a tree diagram to show the total
  outcomes possible.

Blue jeans
T-shirt and blue jeans
T-shirt
Khaki slacks
T-shirt and khaki slacks
Blue jeans
Hoodie and blue jeans
Hoodie
Khaki slacks
Hoodie and khaki slacks
Blue jeans
Sweater and blue jeans
Sweater
Khaki slacks
Sweater and khaki slacks
So there are 6 possible outcomes.
So there are 6 possible outcomes.
2
How many sandwich outcomes are possible if you
have 3 choices of bread, 5
choices of meat, and 3 choices of cheese?
How many choices of bread?
How many choices of meat?
How many choices of cheese?
45 outcomes

3
5
3


At Boatmans Blazing Blades you can special order
any kind of roller-blades you want. There are 4
different boot styles, 10 boot colors, you can
choose 4 or 5 wheels, and wheels come in 5
different colors. How many outcomes are possible
to create?
How many choices of boot styles?
How many choices of boot colors?
How many choices for the of wheels?
How many choices of wheel colors?
400 outcomes
4
10
2
5




3
Fundamental Counting Principle Total
outcomesProduct of the outcomes for each event.
Ex. 1 When you rent ski equipment from Swan Ski
Resort, you choose from 4 different types of ski
boots, 5 lengths of skis, and 2 types of poles.
How many different outfits are possible? 4
5 2 40 different outfits
Ex. 2 What is the probability of winning the
Oklahoma state lottery where the winning number
is made up of four digits from 0 to 9 chosen at
random? How many choices for each digit?
0,1,2,3,4,5,6,7,8,9 10 Each event or digit
will have 10 choices. 10 10 10 10
10,000 Only one number will be the winning
number. P (winning number) 1 / 10,000
0.0001 0.01