Basic Terminology of Probability

Sample Space

denoted S, is the set of all simple events of a probability experiment

Multiplication Rule

For any two events A and B: P(AB) = P(A|B) * P(B) For any two independent events A and B: P(AB) = P(A) * P(B)

Addition Rule

For any two events A and B: P(A∪B) = P(A) + P(B) - P(AB) For any two mutually exclusive events A and B: P(A∪B) = P(A) + P(B)

Simple Event

a most basic outcome for a probability experiment

Event

any collection of simple events in the sample space. Usually denoted with upper case letters from the beginning of the alphabet: A B C etc

Experiment

any planned process of making an observation or taking a measurement

Complement

the complement of any event A, denoted A', is the set of all simple events in the sample space not in event A. The key word in complement is not

Conditional Probability

the conditional probability of event A given event B has occurred, denoted P(A|B), is given by: P(A|B) = P(AB)/P(B), P(B) does not equal 0

Intersection

the intersection of any two events A and B, denoted AB, is the set of all simple events A and B have in common. The key word for intersection is AND.

Probability of an Event

the sum of the simple events included in the events. P(events)

Union

the union of any two events A and B, denoted A ∪ B, is the set of all simple events in A, or B, or both. The key word in union is OR

Independent Events

two events A and B are independent if P(A|B) = P(A)

Mutually Exclusive (m.e.)

two events A and B are mutually exclusive if AB = 0 (i.e. they have no simple events in common)