JEE Mathematics / Probability / Events , Occurrence of events, Certain and Impossible events , Simple and Compound events

1. Physics Helpline
L K Satapathy
Probability Theory 3

2. Physics Helpline
L K Satapathy
Events : Any subset E of the sample space S of a Random Experiment
is called an Event
Consider the experiment of tossing two coins
Sample space of the experiment is S = { HH , HT , TH , TT }
If we are interested in the occurrence of ‘exactly one head’
The corresponding elements of S are HT and TH
 We write the event as E = { HT , TH }
We observe that E is a subset of S
Probability Theory 3

3. Physics Helpline
L K Satapathy
Experiment : Tossing of Two coins  S = { HH , HT , TH , TT }
Description of event Subset of S
At least one tail A = { HT , TH , TT }
At least one head B = { HH , HT , TH }
Examples of events
Description of event Subset of S
Getting an odd number C = { 1 , 3 , 5 }
Getting a prime number D = { 2 , 3 , 5 }
Experiment : Rolling of a die  S = { 1 , 2 , 3 , 4 , 5 , 6 }
Probability Theory 3

4. Physics Helpline
L K Satapathy
We denote the outcome of an experiment by 
Consider an event E of a sample space S  E  S
Occurrence of an Event
If   E , then we say that E has occurred
If   E , then we say that E has NOT occurred
Consider the experiment of throwing a die.  S = { 1 , 2 , 3 , 4 , 5 , 6 }
Consider the event ‘a number less than 4 occurs’  E = { 1 , 2 , 3 }
If the outcome () is 1 , 2 or 3 , then we say that E has occurred
If the outcome () is 4 , 5 or 6 , then we say that E has not occurred
Probability Theory 3

5. Physics Helpline
L K Satapathy
Types of Events :
Certain Event : The Sample space S is a subset of itself
 The event E = S is a certain event
Impossible Event : The empty set  is a subset of sample space S
 The event E =  is an impossible event
Example : Consider the experiment of throwing a die.
The event ‘a number less than 7 occurs’ is a certain event.
(Since all outcomes of the experiment ensure the occurrence of E)
Example : Consider the experiment of throwing a die.
The event ‘a number greater than 7 occurs’ is an impossible event.
(Since no outcome of the experiment ensure the occurrence of E)
Probability Theory 3

6. Physics Helpline
L K Satapathy
Types of Events :
Simple Event :
It is an event which has more than one sample points of S.
In the experiment of tossing two coins , S = { HH , HT , TH , TT }
Consider the experiment of tossing three coins. The sample space
S = { HHH , HHT , HTH , HTT , THH , THT , TTH , TTT }
The event (exactly 1 head) , E = { HTT , THT , TTH } is a compound event
Here n = 4  There are 4 simple events {HH} , {HT} , {TH} and {TT}
If S has n distinct elements , there are n simple events.
It is an event which has only one sample point of S.
Compound Event :
Probability Theory 3

7. Physics Helpline
L K Satapathy
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