To determine the complement of the set of pins that Sam and Silvie knocked down, we first need to identify all the unique scores knocked down by both players in a single frame. We can then determine what pins are not included in that set.
From the data provided, we have:
- Sam's scores: 5, 6, 7, 8, 10, 9, 4, 10, 4, 6
- Silvie's scores: 8, 5, 7, 5, 2, 9, 10, 4, 5, 9
Combining Sam's and Silvie's scores, we get the unique values they knocked down:
- Unique scores: {2, 4, 5, 6, 7, 8, 9, 10}
The complete sample space of possible scores from 1 to 10 is:
- Sample Space: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
To find the complement of the set of pins knocked down by Sam and Silvie (which is {2, 4, 5, 6, 7, 8, 9, 10}), we look for the values in the sample space that are not in this set.
From the sample space, the values that are not in {2, 4, 5, 6, 7, 8, 9, 10} are:
- {1, 3}
Thus, the complement set is {1, 3}.
Out of the provided responses, the correct one is:
{0, 1, 3}
However, since 0 is not a possible score in bowling frames, the ideal response according to the context, since it is a complement of the effective scores (ignoring 0), would just be:
{1, 3}
But it seems the correct answer among the options given, acknowledging the available choice of (including 0 possibly in a set), would be:
{0, 1, 3}