Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Types of Events

(i) Impossible Event:

The empty set  \phi is called Impossible Event.

(ii) Sure Event:

The whole sample space \text{( S )} is called the Sure Event.

(iii) Simple Event

If an event  \text{ E } has only one sample point of a sample space, it is called a Simple (or Elementary) event.

Example:

Tossing two coins, a sample space is:

 \begin{aligned} S &= \left\{ \text{HH,HT,TH,TT} \right\}\\ E_1&=\left\{ \text{HH} \right\} \\E_2&=\left\{ \text{HT} \right\}\\E_3&= \left\{ \text{TH} \right\}\\E_4&=\left\{ \text{TT} \right\} \end{aligned}

(iv) Compound Event:

If an event has more than one sample point, it is called a Compound event.

Example:

“Tossing a Coin twice”, the events

 \text{E} : ‘exactly one head appeared.’

 \text{F} : ‘at least one head appeared.’

 \text{G} : ‘Almost one head appeared’.

Above all events are compound events and the subset of whole sample space  \text{S} .

 \begin{aligned} E&=\left\{ \text{HT,HT} \right\}\\F&=\left\{ \text{HT,TH,HH} \right\}\\G&=\left\{ \text{HT,TH,TT} \right\} \end{aligned}

Each of the above events contains more than one sample point.

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