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# Probability

## 15 PROBABILITY

Experiment:Any activity which results in outcomes is called an experiment.

E.g. tossing a coin,rolling a die.

Event: An outcome of a random experiment is called an event.

FavorableEvent: The favorableoutcome is called favorable event.

e.g.Getting a head, getting even number on die.

Probability of an event:

*

If there are n elementary events associated with a random experiment and m of them are favorable to an event $\text{A}$, then the probability of happening or occurrence of event A is denoted by $\text{P}\left(\text{A}\right)$ and is defined as the ratio $\frac{\text{m}}{\text{n}}$.

Thus,

Elementary event:

An event having only one outcome is called elementary event.

Complimentary event:

For an event $\text{E}$, the event “not” is called complimentary event.

It is denoted by $\overline{\text{E}}$.

e.g.for event “getting even numbers”, the complimentary event is “ getting odd

numbers”

proof: If total no. of outcomes

total no. of favorable outcome of

Total no.of non favorable

Then

And

$\to$

$\to$

$\to$

Sure event:

The event which is sure or which has probability $\text{1}$ is called sure event.

Impossible event:

The event which is not possible or which has probability $\text{0}$ is called impossible event.

Range of probability

$\text{0}\le \text{P}\left(\text{E}\right)\le \text{1}$

As

Clearly, .

$\to$

Sum of probabilities of all elementary:

Sum of probabilities of all elementary events is $\text{1}$.