# Probability: Definition

Let

*S*be the sample space, then the probability of occurrence of an event*E*is denoted by*P*(*E*) and is defined as*P*(

*E*) =

=

Example

When a die is rolled, sample space *S* = {1, 2, 3, 4, 5, 6}.

Let *A* = the event of occurrence of an odd number = {1, 3, 5}.

*B* = the event of occurrence of a number greater than 4 = {5, 6}.

Then *P*(*a*) = and *P*(*b*) = .

# Complement of an event

Complement of an event

*E*is denoted by*E*â€² or*E*^{c}or*.**E*â€² means non-occurrence of event*E*. Thus*E*â€² occurs if and only if*E*does not occur. We have*P*(*E*) +*P*(*E*â€²) = 1.# Odds in favor and odds against an event

Let

*S*be the sample space and*E*be an event. Let*E*â€² denote the complement of event*E*, then- Odds in favor of event
- Odds against an event

**Odds in favor of event**

*Note:**E*=

and odds against event

*E*=