Probability Theory

Let us consider an experiment whose outcomes are non deterministic, particularly, an experiment which has more than one outcomes.

Thus, we are forming the set of all possible outcomes as S, this is called as the sample space.

Let us consider the rolling a six phases die, numbered 1 to 6.

Then the sample space will be

S = { 1 ,2 ,3 ,4 , 5 , 6 }

Any subset of the sample space is called as an ` Event`

Let us consider the set denoted by E, where E = { 2 , 4 , 6}

It is the event denoted by occurrence of even numbers.

Now, if we consider the set as D = { 1 ,2 } then it is defined as the occurrence of the numbers 1 and 2.

All these events are defined on the basis of S or the sample space.

Probability Of an Event :

Let us define an event A, then suppose there are s favorable outcomes for an event A, and the sample space contains n outcomes, then the probability of an event A is defined as n P ( A ) = - s

For, example, let us consider an event f getting an even numbers : Then we have A = { 2.4.6 } and S = {1,2,3,4,5,6}

So, 3 1 P ( A ) = - = - 6 2