The number $1,\,2,\,3$ 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.
The number $1,\,2,\,3$ 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.
If $1$ appears on the first drawn slip, then the possibilities that the number appears on the second drawn slip are $2,\,3,$ or $4 .$ Similarly, if $2$ appears on the first drawn slip, then the possibilities that the number appears on the second drawn slip are $1,\,3,$ or $4 .$ The same holds true for the remaining number too.
Thus, the sample space of this experiment is given by
$S=\{(1,2),\,(1,3)$, $(1,4),\,(2,1)$, $(2,3),\,(2,4),\,(3,1),\,(3,2)$, $(3,4),\,(4,1)$, $(4,2),\,(4,3)\}$
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