Question

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

{0,1,3}
left brace 0 comma 1 comma 3 right brace

{2,6}
left brace 2 comma 6 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

Answer 1

To determine the complement of the set of pins that Sam and Silvie knocked down, we first need to find the set of all the pins they knocked down.

The pins knocked down by Sam are:

• 5, 6, 7, 8, 10, 9, 4, 10, 4, 6

The pins knocked down by Silvie are:

• 8, 5, 7, 5, 2, 9, 10, 4, 5, 9

Now, let's compile the total unique pins they knocked down. The unique values drawn from both Sam's and Silvie's scores are:

• {2, 4, 5, 6, 7, 8, 9, 10}

The sample space for a single bowling frame is:

• {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

The complement of the set of pins knocked down by Sam and Silvie consists of all the values in the sample space that are not in the set they knocked down.

Thus, the pins knocked down (set) is:

• {2, 4, 5, 6, 7, 8, 9, 10}

The sample space is:

• {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Now, the complement will be:

• {1, 3} (since these are the only numbers from the sample space that are not included in the set they knocked down)

Looking at the provided options, we find that the correct complement, which is {1, 3}, is not directly listed. However, if we test the options given, the closest complement that does not contain pins knocked down by either Sam or Silvie is:

The correct answer shouldn't specifically be one of the provided options if it isn't listed exactly as {1, 3}, but based on the definitions, the one closest to complement without including knocked pins is:

{2, 4, 5, 6, 7, 8, 9, 10}, as that retains all which were knocked down and thus leaves too many present.

Meanwhile, given the nature of the responses and question above, remember if we view required pins were below even titled {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} effectively to consider pins bowled excluding therefore is remaining in minus context rather direct pathways to underwriting top sections down this way sets best answers to provision.

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