AP Stats 5.1 and 5.2 Vocab

simulation

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

intersection

The intersection of events A and B, denoted by A ∩ B, refers to the situation when both events occur at the same time.

union

The union of events A and B, denoted by A ∪ B, consists of all outcomes in A, or B, or both.

probability model

A description of some chance process that consists of two parts: a sample space S and a probability for each outcome.

event

Any collection of outcomes from some chance process. That is, an event is a subset of the sample space. Events are usually designated by capital letters, like A, B, C, and so on.

basic probability rules

For any event a, 0 ≤ P(a) ≤ 1. If S is the sample space in a probability model, P(S) = 1. In the case of equally likely outcomes, P(a)= (number of outcomes corresponding to event A)/ (total number of outcomes in sample space) Complement rule: P(aC) = 1 − P(a). Addition rule for mutually exclusive events: If a and B are mutually exclusive, P(a or B) = P(a) + P(B).

general addition rule

If A and B are any two events resulting from some chance process, then the probability that event A or event B (or both) occur is P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

law of large numbers

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

probability

The probability of any outcome of a chance process is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitions.

sample space

The sample space S of a chance process is the set of all possible outcomes.

mutually exclusive (disjoint)

Two events are mutually exclusive (disjoint) if they have no outcomes in common and so can never occur together.

performing a simulation

What is the question of interest about some chance process? Describe how to use a chance device to imitate one repetition of the process. Explain clearly how to identify the outcomes of the chance process and what variable to measure. Perform many repetitions of the simulation. Use the results of your simulation to answer the question of interest.

run

a repetition of the same result

complement

refer to the event "not A"