To determine the complement of the set of pins that Sam and Silvie knocked down, we first need to identify the range of total pins that they knocked down and then find which numbers do not appear in their scores.
Sam knocked down the following pins: 5, 6, 7, 8, 10, 9, 4, 10, 4, 6.
Silvie knocked down the following pins: 8, 5, 7, 5, 2, 9, 10, 4, 5, 9.
Now, let’s collect all the unique values from both of their scores:
Sam's scores: {4, 5, 6, 7, 8, 9, 10}
Silvie's scores: {2, 4, 5, 7, 8, 9, 10}
Combining these, we have the unique values knocked down:
Combined scores: {2, 4, 5, 6, 7, 8, 9, 10}
The sample space of possible scores in a single frame at a bowling game is typically {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Now, to find the complement of the set of pins knocked down by Sam and Silvie, we need to find which pins from the sample space are not in the combined scores:
Sample Space: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Combined scores knocked down: {2, 4, 5, 6, 7, 8, 9, 10}
The pins not knocked down are {0, 1, 3}.
Thus, the complement of the set of pins knocked down by Sam and Silvie is {0, 1, 3}.
The answer is: {0, 1, 3}.