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Probability Defined

The probability of a given event is an expression of likelihood of occurrence of an event. A probability of a given event is a number which ranges from 0 to 1 – zero for an event which cannot occur and 1 for an event which is certain to occur. How the number is assigned would depend on the interpretation of the term ‘probability’. There is no general agreement about its interpretation and many people associate probability and chance with nebulous and mystic ideas. However, broadly speaking there are four different schools of thought on the concept of probability.

(i)    Classical or a priori Probability

The classical approach to probability is the oldest and simplest. It originated in eighteenth century in problems pertaining to games of chance, such as throwing of coins, dice or deck of cards, etc. The basic assumption underlying the classical theory is that the outcomes of a random experiment are “equally likely”.

(ii)    Relative Frequency Theory of Probability

The classical definition is difficult or impossible to apply as soon as we deviate from the fields of coins, dice, cards and other simple games of chance. Secondly, the classical approach may not explain actual results in certain cases.

(iii)    Subjective Approach to Probability

The subjective probability is defined as the probability assigned to an event by an individual based on whatever evidence is available. Hence such probabilities are based on the beliefs of person making the probability statement.

(iv)    Axiomatic Approach to Probability

When this approach is followed, no precise definition of probability is given, rather we give certain axioms or postulates on which probability calculations are based. The whole field of probability theory of finite sample spaces is based upon the following three axioms:

(1)    The probability of an event ranges from zero to one. If the event cannot take place, its probability shall be zero and if it is certain, i.e, bound to occur, its probability shall be one.

(2)    The probability of the entire sample space is 1, i.e., P(S) = 1.

(3)    If A and B are mutually exclusive (or disjoint) events then the probability of occurrence of either A or B denoted by P (AUB) shall be given by:
P(AUB) = P(A) + P(B)
It may be pointed out that out of the four interpretations of the concept of probability, each has its own merits and one may use whichever approach is convenient and appropriate for the problems under consideration.

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