Finite Sample Space:
If a sample space contains a finite number of elements, then the sample space is said to be a finite sample space. The sample space for the experiment of a toss of a coin is a finite sample space. It has only two sample points. But the sample space for the experiment where the coin is tossed until a heads shows up is not a finite sample space -- it is theoretically possible that you could keep tossing the coin indefinitely.