Sample space and event in probability

 Sample space and Event

Sample space: 

A collection of all possible outcomes of an experiment is called sample space.It is denoted by Ω.

Example:

A coin is tossed

 Ω={H,T}

Where H=head, T=tail.

 

Event:

The collection of all outcomes favorable to phenomenon is called an event.

It is denoted by capital letters A,B,C..

Example:

Event A is containing at least one head,if two coins are tossed.

 Ω={HH,HT,TH,TT}

A={HH,HT,TH}

(1) Elementary event:

An event containing only one element is called as elementary or simple event.

Example:

Event A is getting both heads ,if two coins are tossed.

 Ω={HH,HT,TH,TT}

A={HH}

(2) Compound event:

An event which contains more then one sample point of sample space is called a compound event.

Example:

Event A is containing both head and tail,if two coins are tossed.

Ω={HH,HT,TH,TT}

A={HT,TH}

(3)Sure event or certain event:

An event containing all the points of sample space is called sure event.

Example: 

In an experiment of throwing a die ,event A is getting number less than 7.

 Ω={1,2,3,4,5,6}

A={1,2,3,4,5,6,7}

(4)Impossible event:

An event which does not contain any point of sample space is called an impossible event.It is denoted by ϕ 

Example:

 In tossing of two coins ,the event is getting three heads.

(5) Compliment of an event:

The set of all sample points which are belonging to sample space but not ti event A,event A is defined on sample space is called as complementary event of an event A.It is denoted by A'.

Example of compliment event:

Ω={HH,HT,TH,TT}

A={HH}

A'={HT,TH,TT}

(6) Union of two events:

 Let A and B be two events defined on sample space.then the union of A and B is the set of a points that are belonging to either A or in B or both.

It is denoted by A ∪ B

A∪B={x|x€A or x€B or x€both A and B}

(7) Intersection of two event:

 Let A and B be two events defined on sample space.Then the intersection of two events is denoted by A intersection B is the set of all points that belong to both A and B.

A∩B={x|x€Aandx€B}

Ω ={1,2,3,4,5,6}

A={2,4,6}

B={1,2}

A∪B={1,2,4,6}

A∩B={2}

Thanks for reading...

Share to support us...

Content created by - Chandrashekhar Awate and Priyanka Pawar

Thanks for your positive feedback to our blog,we are working on our weak points,comment below if any suggestion for us...