To determine the elements of the sample space for the given experiment of rolling a single die and then tossing a coin, let's break down each part of the experiment.
1. Rolling a single die:
- The possible outcomes when rolling a single die are the numbers 1 through 6. Hence, we have the outcomes: \{1, 2, 3, 4, 5, 6\}.
2. Tossing a coin:
- The possible outcomes when tossing a coin are Heads (H) and Tails (T). Hence, we have the outcomes: \{H, T\}.
Now, to find the sample space of the combined experiment, we need to consider each possible outcome of the die roll followed by each possible outcome of the coin toss. This means we pair each number from the die with both 'H' and 'T'.
Thus, the sample space will consist of:
- 1 followed by H
- 1 followed by T
- 2 followed by H
- 2 followed by T
- 3 followed by H
- 3 followed by T
- 4 followed by H
- 4 followed by T
- 5 followed by H
- 5 followed by T
- 6 followed by H
- 6 followed by T
So, the elements of the sample space are:
[tex]\[
\{1 H, 1 T, 2 H, 2 T, 3 H, 3 T, 4 H, 4 T, 5 H, 5 T, 6 H, 6 T\}
\][/tex]
Therefore, the correct option is:
[tex]\[
\{1 H , 2 H , 3 H , 4 H , 5 H , 6 H , 1 T, 2 T, 3 T, 4 T, 5 T, 6 T\}
\][/tex]
