AP Statistics Notes: Unit 4

Law of Large Numbers

Law of Large Numbers

If we observe more and more repetitions of any change process, the proportion of times that a specific outcome occurs approaches a single value.

If A and B are any two events resulting from some chance process

P(A or B)=P(A)+P(B)-P(A and B)

If two events A and B are mutually exclusive (disjoint) if they have no outcomes in common and so can never occur together

Formula: P(A and B)=

Chance Behavior

Unpredictable in the short run but has a regular and predictable pattern in the long run.

Random Phenomenon

A situation is considered random if individual outcomes are uncertain, yet there is a regular distribution of outcomes observed over a large number of

Law of Averages/Gamblers Fallacy

Occurs when an individual erroneously believes that a certain random event is less likely or more likely to happen based on the outcome of a previous event or series of events.

Simulation

The imitation of chance behavior, based on a model that accurately reflects the situation.

Myth of Short-Run Regularity

The idea that randomness is predictable in the short run, whereas probability truly reflects predictability in the long run.

Myth of the Law of Averages

The belief that random behavior will even out in the long run, which misrepresents the nature of probability.

Event

Any collection of outcomes from some chance process.

Sample Space (S)

The set of all possible outcomes of a chance process.