3.1 ---
Probability experiment (Random experiment)—Random process which generates distinct outcomes
Outcome – A result of a probability experiment
Sample Space – S, The set of all possible outcomes of a probability experiment; Use line method to
denote – S = {#, #, #}
Event – A collection of outcomes from the sample space; Use capital letters at the beginning of the
alphabet to denote them in set notation – E: # > #
Probability of an event, P (A) – relative frequency with which the event A will occur
P (A) can be determined theoretically or empirically (perform experiment and observe how
many times the event occurs
Special types of event –
Null Event, ᶲ -- Event with no outcomes to satisfy it
Simple Event – An event which contains exactly one outcome
Union Event, AᴗB – The event which contains all outcomes which satisfy event A or
event B or both( Read as or)
Intersection Event, AᴖB—The event which contains all outcomes which satisfy both
event A and B (read as and)
Complement of an event, A’ – Event which contains all outcomes in the sample space
which do not satisfy event A (A’ read as not A)
Mutually Exclusive Events – Two events which have no outcomes in common
oComplements and simple events are always mutually exclusive
Independent Events – Two events which are such that knowing whether one event
occurs does not change the probability that the other event occurs
3 Axioms of Probability:
0<P(A)<1
P(S) = 1
P(A) = sum of the probabilities for all simple events whose union is A
oBecause of #2 and #3, the sum of the probabilities of all simple events is 1
Properties of Probability:
Prop 4: If the outcomes in S are equally likely, then P (A) = # of outcomes in A/ # of outcomes in S
Prop 5: Addition Rule for Mutually Exclusive Events: If events A and B are mutually exclusive, then P
(AᴗB) = P (A) + P (B)
