Question

A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?

Answer 1

It is given that a dice is rolled until a six comes up. It can be possible that the number 6 comes up with first throw or it can come up in second throw while first throw can contain any number from 1 to 6 and so on.

Thus, the sample space of this experiment is,

S={ 6,( 1,6 ),( 2,6 ),( 3,6 ),( 4,6 ),( 5,6 ),( 1,1,6 ),( 1,2,6 ),⋯, ( 1,5,6 ),( 2,1,6 ),⋯( 2,5,6 ),⋯,( 5,1,6 ),( 5,2,6 ),⋯ }

Note, there are infinite elements in the sample space as it might take any number of throws for a 6 to come up