# 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 