Reduced Sample Space

Sometimes the sample space S is reduced in size and is called a reduced sample space. The symbol {S_r} may be used for a reduced sample space. Suppose a die has been thrown and we have been informed that the experiment has produced an even face. This type of information is called additional information. Thus the reduced sample space is determined by the additional information.

In this example the information has disclosed that an even face has occurred. If we learn which even face has occurred, then it is no longer a situation of probability. When the information is that the face is even, then there is still something hidden from the experimenter and the actual outcome is not known to the observer. In this case the reduced sample space {S_r} is {S_r} = \left\{ {2,4,6} \right\}.