Probability of an Event

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So far, we have introduced the sample of an experiment and used it to describe events. In this section, we introduce probabilities associated to the events.

If a trial results in n-exhaustive, mutually exclusive and equally likely cases and m of them are favourable to the occurrence of an event A, then the probability of the happening of A, denoted by P(A), is given by

Note 2:

If P(A) = 0 then A is called a null event, or impossible event.

Note 3:

If P(A) = 1 then A is called a sure event.

Note 4:

If m is the number of cases favourable to A. Then

m - n is favourable to "non occurrence of A".

Note 5:

If the odds are a:b in favour of A then

This is the same as odds are b:a against the event A.

Statistical or Empirical Probability

If a trial is repeated N number of times under essential homogeneous

Axiomatic Approach to Probability

Axiomatic approach to probability closely relates the theory of probability to set theory.

Let S be the sample space of an experiment. Probability is a function, which associates a non-negative real number to every event A of the sample space denoted by P(A) satisfying the following axioms.

• For every event A in S, P(A) ³ 0.

• P(S) = 1.

• If A₁, A₂, A₃,….A_n are mutually exclusive events in S, then