1. PROBABILITY

2. Probability – a number that describes how likely an event is to occur.

3. Probability can be expressed as:
- a fraction 1/2 -a decimal .9 - a percent 50%

4. First, this does assume all sides are equally likely to come up
First, this does assume all sides are equally likely to come up. Equally likely- all outcomes have the same chance.

5. Terminology
At random: all outcomes have a equal chance of occurring Favorable outcome: the outcome you want to occur. Possible outcome: all the possible results of an experiment sample space: the set of all possible outcomes ( {1, 2, 3, 4, 5, 6} ) With replacement- returning the outcome to the sample space Without replacement- not restoring an outcome

6. P ( ) = Probability of an event
Example: P (6) means the probability of rolling a six

7. An event that has probability 1 must always happen
An event that has probability 1 must always happen. It is called a sure or certain event. experiment: Toss coin event: heads or tails When you toss a coin, you must get either a heads or a tail. An event that has probability 0 will never happen. It is called an impossible event. experiment: Roll die event: roll 7 When you roll a six-sided die, you cannot get a 7.

8. What is probability?
Probability discusses the likelihood or chance of something happening. For instance, -- the probability of it raining tomorrow -- the probability of rolling a 4 on a six-sided die -- the probability of being struck by lightning -- the probability of pulling an Ace out of a deck of cards -- the probability of meeting your spouse on a blind date

9. Independent events
Two events are independent if the occurrence of one does not affect the occurrence of the other. The events of rolling a “4” on a die and spinning red are independent because the occurrence of the 4 on the die does not affect the probability that I will get an red also.

10. Dependent Events
Two events are dependent if the occurrence of one does affect the occurrence of the other. The events of choosing a King from a deck of cards and then a Queen are dependent because the occurrence of the second is dependent on the first.

11. Theoretical vs. Experimental Probability
Theoretical Probability: - The probability we find on paper. - It is how a probability of an event “should” happen. Experimental Probability: - Experimental probability refers to the probability of an event occurring when an experiment was conducted.

12. Theoretical vs. Experimental Probability
Theoretical Probability: number of favorable outcomes Theoretical Probability= number of possible outcomes

13. Theoretical vs. Experimental Probability
Experimental Probability: number of event occurrences Experimental Probability= Total number of trials

14. Theoretical vs. Experimental Probability
Example 1: Roll a dice.
What is the theoretical probability of rolling a 4?
# favorable outcomes
# possible outcomes 1 6
The probability of rolling a 4 is 1 out of 6

15. Theoretical vs. Experimental Probability
Example 1 Continued: Roll a dice.
What is the experimental probability of rolling a 4?
# event occurrences
Total # of trials

16. Theoretical vs. Experimental Probability
Example 2: Coins.
What is the theoretical probability of flipping a tail?
# favorable outcomes
# possible outcomes 1 2
The probability of spinning green is 1 out of 2 or .5 or 50%

17. Theoretical vs. Experimental Probability
Example 2 Continued: Coins.
What is the experimental probability of flipping a tail?
# favorable outcomes
# possible outcomes