empirical probability of A = n times A occurred

                                        number of trials

OR

algebra = P'(A) = n(A)/n

theoretical prob A = n of times A occurs in sample space

                         n elements in sample space

OR

algebra = P(A) = n(A)

                        n(S)

probability is always a numerical value between 1 and 0

0≤P(A)≤1

sum of the probabilities for all outcomes of an experiment is equal to exactly one

ΣP(A) = 1 for all outcomes

• probabiity represents a relative frequency
• P(A) = ratio of the number of times an event can be expected to happen
• P'(A) = ratio of the number of times an event did occur divided by the number of data
• numerator must be 0 or positive
• denominatior must be greater than zero
• probability will alway be a number between 0 and 1

the odds in favor of an event are a to b (a:b)

• ex) the odds against rain tomorrow are 1 to 4 (1:4)
• the probability of rain tomorrow is 4/(4+1)=4/5= 0.8
• probability that there will be no rain tomorrow is 1/(4+1) = 1/5 = 0.2

relative frequency with which an event can be expected to occur under the condition that additional, preexisting information is known about some other event.

• P(AIB) = probability of event A occurring und the condition that event B is known to already exist

complement of an event A (A), is the set of all sample points in the sample space that do not belong to A

• ex) complement of the event "success" is "failure"

Complement Rule

probability of A complement = one-probability of A

P(A) = 1 - P(A)

• Let A and B be two events defined in a sample space, S

• P(A or B) = P(A) + P(B) - P(A and B)

• A and B be two events defined in sample space, S
• P(A and B) = P(A) x P(BIA)