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

Sample Space and Event

Sample Space:

The sample space of an experiment is the set of all possible outcomes of the experiment.

Example:

Toss a Coin twice. The possible outcome are  \text{hh,ht,th,tt} where  \text{h}= head and  \text{t}= tail. Then the sample space  (\text{S})=\left\{ \text{hh,ht,th,tt} \right\}

An element of the sample space is called an Elementary event.

Event:

A subset of a sample space  \text{ S } (of an experiment) is called an event. An event is said to occur if an element of the event occurs.

Remark:

All sample spaces are finite or countable infinity.

For uncountable Sample Space:

(i)  \text{S} itself is an event.

(ii) The empty set  \phi is an event.

(iii) If  \text{A}\ \text{ and }\ \text{B} are events (that is  \text{A}\subset \text{S}, \text{B}\subset \text{S} ), then  \text{A}\cup \text{B} is an event (that occurs if  \text{A} occurs or  \text{B} occurs).

(iv)  \text{A}\cap \text{B} is an event  A'(=S-A) is an event that occurs when  \text{ A } does not occur.

(v) If  A is an event  A'(=S-A) is an event that occurs when  \text{ A } does not occur.

Example:

Let  A=\left\{ (1,6),(2,5),(3,4),(5,2),(6,1) \right\} which is a subset of  \text{ S } . Clearly,  A can be described as the event that sum of points obtained in two throws of a die is  7 .

Example:

Let  C=\left\{ \text{hht,hth,thh} \right\}

 C can be described as the event of getting exactly  2 heads in tossing a coin three times.

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