Question

The numbers $1,2,3$ and $4$ are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box one after the other without replacement. Describe the sample space for the experiment.

Answer 1

Given number of slips in the box are $4$
$\square \square \square \square$
$1234$
Now, if the person withdraws first slip with number $1$ on it, then in second draw $2,3$ or $4$ is possible.
Similarly, if the person withdraws first slip with number $2$ on it, then in second draw $1,3$ or $4$ is possible.
Similarly, if the person withdraws first slip with number $3$ on it, then in second draw $1,2$ or $4$ is possible.
Similarly, if the person withdraws first slip with number $4$ on it, then in second draw $1,2$ or $3$ is possible.
So, the sample space for the given experiment is
$S=\left\{\right(1,2),(1,3),(1,4),(2,1),(2,3),(2,4),(3,1),(3,2),(3,4),(4,1),(4,2),(4,3\left)\right\}$