Simple Probability Probability Experiment: An action (trial) that has measurable results (counts, measurements, responses). Outcome: The result of a single trial. Sample Space: The set of all possible outcomes. Event: One or more outcomes. A subset of the sample space.

Simple Probability Example: Experiment: Rolling a die Trial: One roll Outcome: The number that shows face up Sample Space: 1, 2, 3, 4, 5, 6 Event: An even number, a one, prime numbers, etc

Simple Probability Experiment: Flip a Coin and Roll a Die. Sample Space: H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6 H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6 H T

Simple Probability Classical (Theoretical) Probability: Identify the event of interest as a success, then

Simple Probability Classical (Theoretical) Probability: Example: Probability of rolling an even number on one die: Success: 2, 4, 6 Outcomes: 1, 2, 3, 4, 5, 6 

Empirical (Experimental) Probability: Simple Probability Empirical (Experimental) Probability:

Simple Probability Empirical (Experimental) Probability: Example: You roll a die seven times: You get: 1, 4, 6, 2, 3, 3, 5 

The Law of Large Numbers Simple Probability The Law of Large Numbers As the number of trials approaches infinity, the theoretical and experimental probability should become the same. In other words, if I flip a coin ten times, I may not (probably won’t) get 50% heads, but if I flip it a million times, I should be pretty close.

Probabilities from a frequency chart: Simple Probability Probabilities from a frequency chart: Grade Frequency A 3 B 7 C 12 D 10 F 2 34 What is the probability that a student drawn at random, made an A? P(A) = 3/34 Student drawn at random, Made less than a C? P(less than C) = 12/34

Complement of an event: Simple Probability Complement of an event: The set of all outcomes where the designated success does not take place: Notated: or

Simple Probability Example of Complement Grade Frequency A 3 B 7 C 12 10 F 2 34 What is the complement of The event: E = C or better? E’ = D or F

Simple Probability Odds Odds are another way of representing probabilities. Probability is defined as: The odds in favor of something happening are defined as: #successes:#failures or #successes to # failures Odds can also be expressed as “odds against”: #failures:#successes or # failures to successes

Simple Probability Example: What is the probability of rolling a four with one die? 1/6 What are the odds in favor of rolling a four with one die? 1:5 What are the odds against rolling a four with one die? 5:1 against

Simple Probability Example: What is the probability of rolling a four with one die? What are the odds in favor of rolling a four with one die? What are the odds against rolling a four with one die?