# Probability of an Event – Formula and Examples

Here you will learn what is the probability of an event formula with examples.

Let’s begin –

## Probability of an Event

Definition : If there are n elementary events associated with a random experiment and m of them are favourable to an event A, then the probability of happening or occurrence of A is denoted by P(A) and is defined as ratio $$m\over n$$.

Thus, Probability of an Event = P(A) = $$number of favourable event\over total number of elementary events$$

$$P(A)$$ = $$m\over n$$

Clearly, 0 $$\le$$ m $$\le$$ n. Therefore,

0 $$\le$$ $$m\over n$$ $$\le$$ 1

$$\implies$$  0 $$\le$$ P(A) $$\le$$ 1

Hence, Probability of event lies between 0 and 1.

If P(A) = 1, then A is called certain event and A is called an impossible event, if P(A) = 0.

The number of elementary events which will ensures the non-occurrence of A i.e. which ensure the occurrence of A’ is (n – m). Therefore,

P(A’) = $$n – m\over n$$

$$\implies$$ P(A’) = 1 – $$m\over n$$

$$\implies$$ P(A’) = 1 – P(A)

$$\implies$$ P(A) + P(A’) = 1

Also Read : Probability Basic Concepts

## Odds in Favour and Against the Occurrence of Event

The odds in favour of occurrence of the event A are defined by m : (n – m) i.e ; P(A) : P(A’)

The odds against the occurrence of A are defined by n – m : m i.e. P(A’) : P(A).

Example : Find the probability of getting a head in a toss of an unbiased coin.

Solution : The sample space associated with the random experiment is S = {H, T}.

$$\therefore$$   Total number of elementary events = 2.

We observe that there are two elementary events viz. H, T associated to the given random experiment. Out of these two elementary events only one is favourable i.e. H.

$$\therefore$$   Favourable number of elementary events = 1

Hence, Required Probability = $$1\over 2$$