Download PROBABILITY HANDOUT

PROBABILITY HANDOUT
DEFN:
A sample space, S, is a listing of all possible outcomes from an experiment.
Listed below are two examples of a sample space for an experiment consisting of
flipping two fair coins:
S = {HH, HT, TH, TT}
S = {No heads, One head, Two heads}
DEFN:
An event, A, is a subset of the sample space.
An experiment consisting of flipping two fair coins includes (but is not limited to) the
following possible events:
A = getting two heads = {HH}
B = getting one head out of two flips = {HT, TH}
C = getting at least one head out of two flips = {HT, TH, HH}
DEFN:
The complement of Event A is everything in the sample space that is not A. The
complement of A is denoted A .
Notation:P(A) is read “the probability of event A’ and is the likelihood that event A will occur.
Facts:
0 ≤ P(A) ≤ 1
P(S) = 1
P(A) + P( A ) = 1
Notation:P(A|B) is read “the probability of A given B” and is the conditional probability of
event A occurring given that event B has occurred. This concept allows us to
implement additional knowledge into our models.
DEFN:
The union of events A and B is the set of all elements that occur in either A OR B (or
both). The union of events A and B is denoted (A or B).
DEFN:
The intersection of events A and B is the set of all elements that are common to both A
AND B. The intersection of events A and B is denoted (A and B).
DEFN:
Events A and B are said to be mutually exclusive if the occurrence of one events
precludes the occurrence of the other event. If events A and B are mutually exclusive
then: P(A and B) = 0; P(A|B) = 0; P(B|A) = 0.
DEFN:
Events A and B are said to be independent if the occurrence of one event does not
affect the probability of occurrence of the other event. If events A and B are
independent then:
P(A|B) = P(A); P(B|A) = P(B).
RULES:
Additive Rule:
P(A or B) = P(A) + P(B) – P(A and B)
Multiplicative Rule:
P(A and B) = P(A) * P(B|A)
= P(B) * P(A|B)