$A$ coin is tossed. If it shows a tail,we draw a ball from a box which contains $2$ red and $3$ black balls. If it shows a head,we throw a die. Find the sample space for this experiment.

The box contains $2$ red balls and $3$ black balls. Let us denote the $2$ red balls as $R_{1}, R_{2}$ and the $3$ black balls as $B_{1}, B_{2}, B_{3}$.
The sample space $S$ of this experiment is the set of all possible outcomes.
If the coin shows a tail $(T)$,we draw a ball from the box,resulting in outcomes: $TR_{1}, TR_{2}, TB_{1}, TB_{2}, TB_{3}$.
If the coin shows a head $(H)$,we throw a die,resulting in outcomes: $H1, H2, H3, H4, H5, H6$.
Therefore,the sample space is $S = \{TR_{1}, TR_{2}, TB_{1}, TB_{2}, TB_{3}, H1, H2, H3, H4, H5, H6\}$.