### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: 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 where head and tail. Then the sample space An element of the sample space is called an Elementary event.

Event:

A subset of a sample space (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) itself is an event.

(ii) The empty set is an event.

(iii) If are events (that is ), then is an event (that occurs if occurs or occurs).

(iv) is an event is an event that occurs when does not occur.

(v) If is an event is an event that occurs when does not occur.

Example:

Let which is a subset of . Clearly, can be described as the event that sum of points obtained in two throws of a die is .

Example:

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

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