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:
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.

Four slips marked as $1,2,3,4,$ are put in the box and mixed up.
A person draws two slips one after other without replacement. So, $(1,1),(2,2),(3,3)$ and $(4,4)$ are not possible.
Hence the required sample space is
$S=\left\{\right(1,2),(1,3),(1,4),(2,1),(2,3),(2,4),(3,1),(3,2),(3,4),(4,1),(4,2),(4,3\left)\right\}$.