Download Probability Rules

Probability Rules
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Rule 1.
The probability of any event (A)
is a number between zero and
one.
0 < P(A) < 1
Probability Rules

Rule 2.
The sum of the probabilities of
all basic outcomes in the
sample space must equal one
P(S)=P(e1)+P(e2)+P(e3)+....+P(en)=1
Probability Rules

Rule 3.
The probability of the union of
two basic outcomes is equal to
the sum of the probabilities of
the individual events
If
E1 = (e1, e2, e3)
then, P(E1) = P(e1) + P(e2) + P(e3)
Probability Rules
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Rule 4.
The Complement of an event is
the remainder of the sample
space beyond the event
P (A) = 1 - P (A)
Probability Rules
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Rule 5.
The Addition Rule describes the
probability for the union of two
events as the sum of marginal
probabilities minus their joint
(common) probability
P(AUB)  P(A)  P(B)  P(AI B)
P(A or B) = P(A) + P(B) - P(A and B)
Probability Rules
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Rule 6.
Addition Rule for mutually
exclusive events A and B
P(AUB) = P(A) + P(B)
P(A or B) = P(A) + P(B)
Probability Rules
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Rule 7.
Conditional probability for any
two events, A and B, is
P(AI B)
P(A \ B) 
P(B)
P (A given B) = P (A and B) / P (B)
where, P (B) is not equal to zero
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Probability Rules
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Rule 8.
Conditional probability for
independent events, A and B, is
P (A \ B) = P (A), and
P (B \ A) = P (B)
Probability Rules
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Rule 9.
Multiplication rule for two Events,
A and B, is
P (A and B) = P (A) * P (B \ A), or
P (B and A) = P (B) * P (A \ B)
Probability Rules
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Rule 10.
Multiplication rule for
independent events, A and B, is
P (A and B) = P (A) * P (B)