Download Probability Rules Formula Sheet

PROBABILITY RULES
Probability Rules
Rule 1: 0 ≤ P(A) < 1
Rule 2: If S is the sample space then P(S) = 1
Rule 3: In the case of equally likely outcomes
P( A) 
Rule 4: Complement
number of outcomes corresponding to event A
total number of outcomes in sample space
P(Ac) = 1 – P(A)
Rule 5: Two events A and B are disjoint (also mutually exclusive)
DISJOINT EVENTS ARE NEVER INDEPENDENT
If they have no common outcomes
P(A or B) = P(A) + P(B) called addition rule for disjoint
GENERAL ADDITION RULE
P(A or B) = P(A) + P(B) – P(A and B)
Rule 6: Two events A and B are independent if knowing that one
event occurs does not change the probability that the
other occurs
P(A and B) = P(A)•P(B)
called the multiplication rule for
Independent events
GENERAL MULTIPLICATION RULE
P(A and B) = P(A)•P(B│A) B occurs given A occurred
Conditional Probability P B l A  =
THREE INDEPENDENCE “Rules”
P(A and B) = P(A)•P(B)
and
P(A│B) = P(A)
P(B│A) = P(B)
P  A and B  P(both events occur )
=
PA
P  given event occurs 