In this Chapter, we studied about the axiomatic approach of probability.

The main features of this Chapter are as follows:

* Sample space:* The set of all possible outcomes

*Elements of sample space*

**Sample points:***A subset of the sample space*

**Event:***The empty set*

**Impossible event :***The whole sample space*

**Sure event:*** Complementary event or ‘not event’* : The set A′ or S – A

* Event A or B:* The set A ∪ B

*The set A ∩ B*

**Event A and B:***The set A – B*

**Event A and not B:***A and B are mutually exclusive if A ∩ B = φ*

**Mutually exclusive event:***All outcomes with equal probability*

**Equally likely outcomes:***For a finite sample space with equally likely outcomes*

**Probability of an event:**Probability of an event \( P(A) = \frac{n(A)}{n(S)} \), where n(A) = number of elements in the set A,

n(S) = number of elements in the set S.

If A and B are any two events, then

P(A or B) = P(A) + P(B) – P(A and B) equivalently,

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

If A and B are mutually exclusive, then P(A or B) = P(A) + P(B)

If A is any event, then P(not A) = 1 – P(A)