# 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