Probability and its postulates

Probability, which gives the likelihood of occurrence of an event, is denoted by P.

Let S denote the sample space of a random experiment, the basic outcomes, and A an event. The probability that an event A will occur is denoted by .

The probability has the following important properties:

1. If A is any event in the sample space S, then .

An event that can not occur has zero probability; such event is called an impossible event. An event that is certain to occur has a probability equal to 1 and is called sure event.

For impossible event M: P (M) =0

For a sure event C: P (C) =1

2. Let A be an event in sample space S, and let denote the basic outcomes. Then

,

where the notation implies that the summation extends over all the basic outcomes in A.

3. The sum of the probabilities for all the basic outcomes in the sample space always is 1.Thus

.

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