Question Sam and Silvie go bowling. The following table shows how many total pins they knocked down in each of the 10 frames. Sam 5 6 7 8 10 9 4 10 4 6 Silvie 8 5 7 5 2 9 10 4 5 9 If the sample space is all of the possible numbers of pins that can be knocked down in a single frame, which subset would be considered a complement of the set of pins that Sam and Silvie knocked down? (1 point) Responses {1,2,3,4,5,6,7,8,9,10} left brace 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 right brace {2,6} left brace 2 comma 6 right brace {0,1,3} left brace 0 comma 1 comma 3 right brace {2,4,5,6,7,8,9,10} left brace 2 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 right brace

1 answer

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}