Example 3 Tossing a fair coin until a head is obtained

We may have to toss the coin any number of times before a head is obtained. Thus the possible outcomes are :
                H, TH,TTH,TTTH, …..
How many outcomes are there? The outcomes are countable but infinite in number. The countably infinite sample space is .

Example 4 Picking a real number at random between -1 and +1

The associated sample space is

Clearly is a continuous sample space.

Example 5 Output of a radio receiver at any time

Suppose the output voltage of a radio receiver at any time t is a value lying between -5 V and 5V.
           The associated sample space is continuous and given by
                                
           Clearly is a continuous sample space.

The probability of an event is a number assigned to the event. Let us see how we can define probability.