1. Probability

2. Vocabulary Outcome: any of the possible results of an action
Example: 1
Sample Space: Set of all possible outcomes
Example: 1,2,3,4,5,or 6

3. Example
Create a tree diagram for rolling the dice. Dice 1 2 3 4 5 6

4. Example
Create a tree diagram for the spinner

5. Probability of Simple Events
Probability: chance that some event will occur
Example: rolling a 6
Simple Event: one outcome or collection of outcomes

6. Example What is the probability of getting a red hat?
1 red hat out of 4 hats
0.25
25%

7. Example
What is the probability of rolling a 6 on the dice?

8. Theoretical vs. Experimental
Theoretical Probability
Experimental Probability
What should happen when conducting an experiment
What actually happens when conducting an experiment

9. If you flip a coin ten times what is the theoretical probability of getting heads?
Desired Outcome 1
Sample Space 2 X
You should get heads 5 times out of the ten tries.
Step 1 Step 2: set up proportion Step 3: Cross Multiply

10. Example
If you spin this spinner 20 times, what is the theoretical probability of getting green?

11. Example
If you have a coin and flip it 20 times what is the probability of getting heads?

12. Independent Vs. Dependent
Independent Probability
Dependent Probability
When one event does not affect the other event
Example:
When one event affects the other event
Do Not Replace

13. Identify
With Replacing
Without Replacing
Without Replacing

14. Example Independent
A number cube is rolled and a marble is selected at random from the bag. Determine P(even and yellow).
Step 1: determine the probability of each event.
P(even) = 3/6 = ½
P(yellow) = 2/8 = ¼
Step 2: multiply P(even) X P(yellow)
P(even and yellow) = ½ X ¼
P(even and yellow)= 1/8

15. Example Dependent
Tina randomly selects a marble from the bag shown and then Nathan selects a marble randomly. What is the probability that both will get a green marble?
Step 1: determine the probability of Tina choosing a green marble.
P(Tina green) = 2/8 = ¼
Step 2: determine the probability of Nathan choosing a green marble also.
P(Nathan green) = 1/7
Tina did not replace the green marble
Step 3: Multiply P(Tina green) X P(Nathan green)
P(both green) = ¼ X 1/7
P(both green)= 1/28