Question

A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?

Answer 1

Given:
A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number, the die is thrown again.
If a coin is tossed then possible outcomes are $(H,T)$
If a die is rolled then possible outcomes are $(1,2,3,4,5,6)$

If a coin is tossed,
$\left(i\right)$
$\left(a\right)$ If head comes then a die is thrown. The possible outcomes are $\left\{H1,H2,H3,H4,H5,H6\right\}$
$\left(b\right)$ If dice shows a even number $H2,H4$ and $H6$, then again a die is thrown.
Then possible outcomes are $=\left\{\begin{array}{cccccc}H21,& H22,& H23,& H24,& H25,& H26,\\ H41,& H42,& H43,& H44,& H45,& H46,\\ H61,& H62,& H63,& H64,& H65,& H66\end{array}\right\}$.

$\left(ii\right)$ if tail comes then possible outcome is $\left(T\right)$
Hence the required sample space is
$S=\left\{\begin{array}{cccccc}& T,& H1,& H3,& H5,& \\ H21,& H22,& H23,& H24,& H25,& H26,\\ H41,& H42,& H43,& H44,& H45,& H46,\\ H61,& H62,& H63,& H64,& H65,& H66\end{array}\right\}$.