$A$ 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?
(N/A) When a coin is tossed,the possible outcomes are head $(H)$ and tail $(T)$.
When a die is thrown,the possible outcomes are $1, 2, 3, 4, 5,$ or $6$.
If the coin shows $T$,the experiment ends.
If the coin shows $H$,a die is thrown. If the result is odd $(1, 3, 5)$,the experiment ends.
If the result is even $(2, 4, 6)$,the die is thrown again.
Thus,the sample space $S$ is:
$S = \{T, H1, H3, H5, H21, H22, H23, H24, H25, H26, H41, H42, H43, H44, H45, H46, H61, H62, H63, H64, H65, H66\}$
When a die is thrown,the possible outcomes are $1, 2, 3, 4, 5,$ or $6$.
If the coin shows $T$,the experiment ends.
If the coin shows $H$,a die is thrown. If the result is odd $(1, 3, 5)$,the experiment ends.
If the result is even $(2, 4, 6)$,the die is thrown again.
Thus,the sample space $S$ is:
$S = \{T, H1, H3, H5, H21, H22, H23, H24, H25, H26, H41, H42, H43, H44, H45, H46, H61, H62, H63, H64, H65, H66\}$
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