Mathematical Classical A Priori Definition of Probability 
Mathematical Classical A Priori Definition of Probability 
A Priori 
In the sense in which it is used in the subject of probability, it means
We come to such a conclusion on the acceptance of the notion that the die behaves in an unbiased manner and that the six elementary events are equally likely.
Our conclusions are based on conclusions drawn by earlier studies or by logical reasoning.
The Mathematical or classical definition of probability is an "a priori" definition.
Mathematical/Classical/APriori definition of Probability 
Probability of Occurrence of Event "A"  = 
 
⇒ P(A)  = 


Therefore,
Probability of Success for Event "A"  = 
 
⇒ P(A)  = 


Probability of Nonoccurrence of an Event 
Where A^{c} represents the event of the nonoccurrence of the Event A,
Number of unfavourable/unfavorable choices for the event  =  Total number of possible choices in the experiment  Number of favourable/favorable choices for the event. 
⇒ m_{A}^{c}  =  n  m_{A} 

Probability of NonOccurrence of Event A  = 
 
⇒ P(A^{c})  = 


Therefore,
Probability of Failure of Event A  = 
 
⇒ P(A^{c})  = 


Probability of occurrence + Probability of Nonoccurrence = 1 
The events of occurrence (success) and nonoccurrence (failure) are mutual complimentaries.
⇒ Probabilities of occurrence and nonoccurrence of an event are complimentaries
(Or) Probabilities of success and failure for an event are complimentaries
We know, P(A^{c})  = 
 
= 
 
= 
 
=  1  P(A) 
⇒ P(A) + P(A^{c}) = 1
The sum of probabilities of occurrence and nonoccurrence of an event is 1.
⇒ For any event, Probability of occurrence + Probability of nonoccurrence = 1
For any event,
Probability of occurrence + Probability of nonoccurrence = 1
⇒ Probability of success + Probability of failure = 1
Probability (classical/mathematical definition)  Formula Interpretation 
They can be either positive or zero (Zero is neither negative nor positive).
It cannot be Zero as it amounts to saying there are no outcomes in the experiment.
Therefore,
the ratios 
 [P(Event)] and 
 [P(Event^{c})] are nonnegative rational numbers 
m = 0, when there are no favourable/favorable choices for the event.
m = n, when all the possible choices form favourable/favorable choices for the event.
Therefore,
the value of 
 ranges between 0 { 
 } and 1 { 
 } 
⇒ The value of P(Event) ranges between 0 and 1 (0 = P(Event) = 1).
P(Event^{c})  =  1  P(Event)  
=  1  (When P(Event) = 0)  
=  0  (When P(Event) = 1) 
⇒ The value of P(Event^{c}) ranges between 0 and 1 (0 = P(Event^{c}) = 1)
Event "A" is called a certain event, if P(A) = 1.
Event "A" is called an impossible event, if P(A) = 0.
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