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.