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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

{2,4,5,6,7,8,9,10}
left brace 2 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 right brace

{2,6}

1 answer

To determine the complement of the set of pins that Sam and Silvie knocked down, we first need to identify the total set of possible outcomes (the sample space) and the actual outcomes from the game.

Sample Space: The sample space for bowling can be a range of scores based on the pins that can be knocked down in a single frame. In this case, the possible number of pins that can be knocked down in one frame is from 0 to 10. Therefore, the sample space is:

\[ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} \]

However, since they can only knock down between 1 and 10 pins in a frame when scoring in bowling, we specifically consider:

\[ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} \]

Knocked Down Pins: Next, let's determine the pins knocked down by both Sam and Silvie over the 10 frames.

  • 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 these scores and identifying the unique values:

  • Sam: {4, 5, 6, 7, 8, 9, 10}
  • Silvie: {2, 4, 5, 7, 8, 9, 10}

Putting together:

  • Combined unique scores = {2, 4, 5, 6, 7, 8, 9, 10} (since 2 was uniquely contributed by Silvie).

Complement: The complement consists of all the scores that are not represented in the set of scores knocked down by Sam and Silvie. From the sample space {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, we have already knocked down {2, 4, 5, 6, 7, 8, 9, 10}.

Now we find the complement as follows:

  • The only number from the sample space that is not present in the combined unique scores is 1 and 3.

Thus, the complement set is:

\[ {1, 3} \]

Looking at the options presented:

  1. {1,2,3,4,5,6,7,8,9,10}
  2. {0,1,3}
  3. {2,4,5,6,7,8,9,10}
  4. {2,6}

The correct answer is evidently missing specifically as there isn't a direct option for {1, 3}. However, none of the provided subsets contain only the numbers that are not knocked down.

Thus, highlighting completeness of the original option, if we're asked for the closest option which includes necessary format or misinterpretation based on typical bowling score system:

The response is not completely accurate since the actual complement {1, 3} isn't offered but numbers must filter down explicitly from choices leading to the realization that none apply exactly.