Experiments, Sample Spaces, and Events Section 7.1 Experiments, Sample Spaces, and Events

Terminology An experiment is an activity with observable results (called outcomes). A sample point is an outcome of an experiment. The sample space is the set of all possible sample points. An event is a subset of a sample space.

Outcomes: landing with a 1, 2, 3, 4, 5, or 6 face up. Ex. Rolling a die Outcomes: landing with a 1, 2, 3, 4, 5, or 6 face up. Sample Space: S ={1, 2, 3, 4, 5, 6} Events: Impossible event Certain event

Ex. An experiment consists of spinning the hand on the disk below two times. Find the sample space. S = {(P,C), (P,W), (P,P), (C,P), (C,W), (C,C), (W,P), (W,C), (W,W)}

Events The union of events A and B is the event The intersection of events A and B is the event The complement of event A is the event AC. Ex. Rolling a die. S = {1, 2, 3, 4, 5, 6} Let A = {1, 2, 3} and B = {1, 3, 5}

Events A and B are mutually exclusive if Ex. When rolling a die, if event A = {2, 4, 6} (evens) and event B = {1, 3, 5} (odds), then A and B are mutually exclusive. Ex. When drawing a single card from a standard deck of cards, if event A = {heart, diamond} (red) and event B = {spade, club} (black), then A and B are mutually exclusive.