Probability Definitions

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The term probability has been interpreted in terms of four definitions :

1. Classical Definition of Probability: the classical definition states that if an experiment consists of ’S’ outcomes that are mutually exclusive, exhaustive, and equally likely and S_A of them ate the favorable outcomes of an event A then the probability of the event is 

P\left( A \right)\; =\; \frac{S_A}{S}

In other words, the probability of event A is equal to the ratio of the number of favorable outcomes S_A to the total number of outcomes.

2. Axiomatic Definition of Probability: In the axiomatic definition of probability, the probability of outcome A is defined by a number assigned to A, such a number satisfies the following axioms: 

a) P\left( A \right)\; \geq \; 0  i.e.,  P(A) should be non-negative.

b) The probability of certain event A = 1. i.e., P(A) = 1

c) If the two events A and B are mutually exclusive then the probability of the event (A \cup B) is P\left( A\cup B \right)\; =\; P\left( A \right)\; +\; P\left( B \right)\;

3. Empirical Definition of Probability: In N trials of a random experiment of an event is found to occur m times then the relative frequency of occurrence of the event is \frac{m}{N} is the limiting value approaches to P. When N increases to infinity then P is called the probability of event A.

i.e., P(A) =\lim_{x \to \infty} (\frac{m}{N})

4. Subjective Definition of probability: In subjective interpretation of probability the number P(A) is assigned to a statement which is a measure of our state of knowledge or belief concerning the truth of A. These kinds of probability are more often used in our day-to-day life and conversation.


 

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