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)