Laws of Probability

Theorem 1

If A and B are events associated with a random experiment having sample space S and if , then



If A and B are mutually exclusive events associated with a random experiment having sample space S, then

If are mutually exclusive events associated with a random experiment, then

Theorem 2

If A and B are mutually exclusive and exhausive events associated with a random experiment having sample space S, then



If are mutually exclusive and exhaustive events associated with random experiment having sample space S, then

Theorem 3

If A and B are any two events associated with a random experiment having sample space S, then

Theorem 4

If A and B are any two events associated with a random experiment, then











Probability of occurence of A only



Probability of occurence of B only





is the probability of occurence of only (or exactly) one of the two events A and B.

Theorem 5

If A, B and C are any three events associated with a random experiment, then

Other Important Properties







If odds in favour of an event A are a:b then


If odds against an event A are a:b then


If probability of an event is p then odds in favour are

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