An experiment consists of rolling a die and then tossing a coin if the number on the die is even. If the number on the die is odd,the coin is tossed twice. Write the sample space for this experiment.
(N/A) die has six faces numbered from $1$ to $6$. Among these,$2, 4,$ and $6$ are even numbers,while $1, 3,$ and $5$ are odd numbers.
$A$ coin has two faces: head $(H)$ and tail $(T)$.
If the number is even,the outcome is (number,coin face). If the number is odd,the outcome is (number,coin face $1$,coin face $2$).
The sample space $S$ is:
$S = \{(2, H), (2, T), (4, H), (4, T), (6, H), (6, T), (1, H, H), (1, H, T), (1, T, H), (1, T, T), (3, H, H), (3, H, T), (3, T, H), (3, T, T), (5, H, H), (5, H, T), (5, T, H), (5, T, T)\}$
$A$ coin has two faces: head $(H)$ and tail $(T)$.
If the number is even,the outcome is (number,coin face). If the number is odd,the outcome is (number,coin face $1$,coin face $2$).
The sample space $S$ is:
$S = \{(2, H), (2, T), (4, H), (4, T), (6, H), (6, T), (1, H, H), (1, H, T), (1, T, H), (1, T, T), (3, H, H), (3, H, T), (3, T, H), (3, T, T), (5, H, H), (5, H, T), (5, T, H), (5, T, T)\}$
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