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9.1 Understanding Probability
Remember to Silence Your Cell Phone and Put It In Your Bag!
Defining ProbabilityThe use of numbers to describe the chance that something will happen.
The ratio of favorable occurrences to the number of total possible occurrences of an observable event.
For this class, unless asked to do
differently, write your probabilities as simplified fractions
TerminologyExperimentOutcomeSample SpaceEqually LikelyUniform Sample SpaceNonuniform Sample SpaceEvent
ExampleUniform Sample Space
ExampleNonuniform Sample Space
Defining Probability (cont.)
Probability, P, of an event A for a uniform sample space:
Probability, P, of an event A for a nonuniform sample space:
SspacesampletheinoutcomestheofallofMeasureAeventthewithassociatedoutcomestheofMeasure
AP )(
SspacesampletheinoutcomesofNumberAeventthewithassociatedoutcomesofNumber
AP )(
Terminology (cont.)
Random EventCertain EventImpossible EventComplementary EventsMutually Exclusive EventsNon-mutually Exclusive Events
Properties of Probability1. 0 P(A) 12. The sum of the probabilities of all
outcomes in the sample space is 1
3. P(a certain event) = 14. P(an impossible event) = 05. If A and B are complementary
events, P(A) = 1 – P(B)
Properties of Probability (cont.)
6. If A and B are mutually exclusive events, P(A or B) = P(A) + P(B)
7. If A and B are non-mutually exclusive events, P(A or B) = P(A) + P(B) – P(A and B)
Law of Large NumbersEmpirical ProbabilityTheoretical Probability
Law of Large Numbers If an experiment is repeated many
times, the empirical probability of an event will approach the theoretical probability of the event occurring.