Question

A die is thrown repeatedly until a six comes up, then the sample space for this experiment is:

• A. $\left\{\right(6),(1,6),(2,6),(3,6),(4,6),(5,6),(6,6),(1,6,6),(1,6,6)...\}$
• B. $\left\{\right(1,6),(2,6),(3,6),(4,6),(5,6),(1,1,6),(1,2,6)...\}$
• C. $\left\{\right(6),(1,6),(2,6),(3,6),(4,6),(5,6),(6,6),(1,1,6),(1,2,6)...\}$
• D. $\left\{\right(6),(1,6),(2,6),(3,6),(4,6),(5,6),(1,1,6),(1,2,6)...\}$

Answer 1

The correct option is D $\left\{\right(6),(1,6),(2,6),(3,6),(4,6),(5,6),(1,1,6),(1,2,6)...\}$

Let us assume that $1,2,3,4,5$ and $6$ are the possible outcomes when the die is thrown.
As per the condition given in the question, a die is thrown repeatedly until a six comes up.
Six may come up for the first throw or six may come up on second throw, and this process will go on continuously until six comes up.
The sample space when $6$ comes on very first throw is $S_1=\left\{6\right\}$
The sample space when $6$ comes on second throw is $S_2=\left\{\right(1,6),(2,6),(3,6),(4,6),(5,6\left)\right\}$

This event can go on for infinite times.
So, the sample space is infinitely defined and it can be given as:
$S=\left\{\right(6),(1,6),(2,6),(3,6),(4,6),(5,6),(1,1,6),(1,2,6)...\}$