Question

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 head, we throw a die. Find the sample space for this experiment.

Answer 1

Given : 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 head, we throw a die.

Consider $(R_1,R_2)$ be the red balls and $(B_1,B_2,B_3)$ be the black balls
If a dice is rolled then possible outcomes are $(1,2,3,4,5,6)$
If a coin is tossed
$\left(a\right)$ If tail comes then we draw a ball from box containing $2$ red and $3$ black balls the possible outcomes are $=\{T{R}_1,T{R}_2,T{B}_1,T{B}_2,T{B}_3\}$
$\left(b\right)$ If head comes, we throw a die then the possible outcomes are $=\{H1,H2,H3,H4,H5,H6\}$
Hence the required sample space is
$S=\left\{\begin{array}{c}T{R}_1,T{R}_2,T{B}_1,T{B}_2,T{B}_3,H1,H2,H3,H4,H5,H6\end{array}\right\}$