ProbabilityExperiments, Sample Spaces, and Events(II.B.1a,1c)Definition of Probability (II.B.1b,1d,2,3a)Rules of Probability (II.B.3)Counting Techniques Used in Probability (II.B.4)Conditional Probability and Independent Events(II.B.4a,4b,4c)Bayes’ Theorem (II.B.4d)

ExperimentsActivities with observable results.Results are known as outcomes.Examples:a)Tossing a coin and noting the side landinguppermost.b)Rolling a six-sided die and noting the numbershowing uppermost.c)Choosing a piece of candy from a bowl and notingthe type of candy selected.

Sample Points, Sample Spaces and EventsA sample pointis an outcome of an experiment.It is an elementof a set.The sample space(S) is the set consisting of all possiblesample points of an experiment.It is a universal set.An event is a collection of sample points from an experiment.It is a subsetof the sample space.An event is said to occur whenever the event contains theobserved outcome.

Types of Sample SpacesFiniteSample SpacesThe experiment has a finite number of possible samplepoints (or outcomes).All sample points can explicitly be listed.Non-FiniteSample SpacesThe experiment has an infinite number of possiblesample points.

Example: You toss a fair coin and note which side landsuppermost.a)Describe the sample space associated with thisexperiment.b)What are the sample points?c)What are the events?

Mutually Exclusive EventsEvents that cannot occur at the same time.They do not share any common sample points.Two events, Aand B, are mutually exclusiveif.Example: In the previous coin example, are anynon-empty events mutually exclusive?