Probability AP Stat Vocab

Intersection

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

Union

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

Probability

The __________ 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.

Simulation

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

Basic Probability Rules (Fill in the blank - no word bank)

(1) For any event a, 0 ≤ P(a) ≤ 1. (2) If S is the sample space in a probability model, P(S) = 1. (3) In the case of equally likely outcomes, P(A) = # of outcomes corresponding to event A /total # of outcomes in sample space (4) Complement rule: P(aC) = 1 − P(a). (5) Addition rule for mutually exclusive events: If a and B are mutually exclusive, P(a or B) = P(a) + P(B).

Complement

A _____ of an Event A^c refers to the even "not A". OR The ______ aC contains exactly the outcomes that are not in a. Complement Rule = The probability that an event does not occur is 1 minus the probability that the event does occur. In symbols, P(AC) = 1 - P(A).

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 ____ is a subset of the sample space. ____ are usually designated by capital letters, like A, B, C, and so on.

General Addition Rule for Two Events

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).

Multiplication Rule of Independent Events

If A and B are independent events, then the probability that A and B both occur is P(A ∩ B) = P(A) · P(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.

Disjoint

Mutually Exclusive

Condition Probability (formula)

P (B|A) = P(A ∩ B)/ P(A)

S

Sample Space

General Multiplication Rule

The probability that events A and B both occur can be found using the formula P(A ∩ B) = P(A) · P(B | A) where P(B | A) is the conditional probability that event B occurs given that event A has already occurred.

Conditional Probability

The probability that one event happens given that another event is already known to have happened. Suppose we know that event A has happened. Then the probability that event B happens given that event A has happened is denoted by P(B | A).

Sample Space

The set of all possible outcomes of a chance process.

Independent

Two events are _ if the occurrence of one does not affect the probability of the other.

Mutually Exclusive

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

Tree Diagram

Used to display the sample space for a chance process that involves a sequence of outcomes.

Venn Diagram

can be used to illustrate the sample space of a chance process