**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:**

* $\text{p}\left(\text{E}\right)\text{=}\frac{\text{numberofoutcomesoffavourabletoE}}{\text{Numberofallpossibleoutcoesoftheexperiment}}$

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, $\text{P}\left(\text{A}\right)\text{=}\frac{\text{m}}{\text{n}}$

**Elementary
event:**

An event having only one outcome is called elementary event.

For e.g .getting a head

**Complimentary
event:**

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

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

$\text{P(}\overline{\text{E}}\text{)=1-P}\left(\text{E}\right)$

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

numbers”

**proof: If
total no. of outcomes **$\text{=n}$

** **

**total no. of favorable
outcome of **$\text{A=m}$

** **

**Total no.of
non favorable **$\text{=n-m}$

** **

Then $\text{P}\left(\text{A}\right)\text{=}\frac{\text{m}}{\text{n}}$

And $\text{P(}\overline{\text{A}}\text{)=}\frac{\text{n-m}}{\text{n}}$

$\to $ $\text{P(}\overline{\text{A}}\text{)=1-}\frac{\text{m}}{\text{n}}$

$\to $ $\text{P}\left(\overline{\text{A}}\right)\text{=1-P}\left(\text{A}\right)$

$\to $ $\text{P}\left(\overline{\text{A}}\right)\text{+P}\left(\text{A}\right)\text{=1}$

** **

**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 $\text{P}\left(\text{A}\right)\text{=}\frac{\text{m}}{\text{n}}$

Clearly, $\text{0}\le \text{mn}$.

$\text{0}\le \frac{\text{m}}{\text{n}}\text{1}$

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

**Sum
of probabilities of all elementary:**

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

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