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

{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

{1,2,3,4,5,6,7,8,9,10}
left brace 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 right brace

Answer 1

To determine the complement of the set of pins that Sam and Silvie knocked down in bowling, we first need to identify the possible total pins knocked down in a frame.

In bowling, a player can knock down between 0 and 10 pins in a single frame. Therefore, the sample space of possible pin counts is: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Next, let’s find the total set of pins knocked down by both Sam and Silvie across their frames:

- Sam's frames: 5, 6, 7, 8, 10, 9, 4, 10, 4, 6
- Silvie's frames: 8, 5, 7, 5, 2, 9, 10, 4, 5, 9

The complete set of pins knocked down (combining both Sam and Silvie) is:
{2, 4, 5, 6, 7, 8, 9, 10} (the values 0, 1, 3 are not included).

The complement of this set would be those elements in the sample space {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} that are not in the set of pins knocked down by Sam and Silvie.

Thus, the complement set from the sample space is:
{0, 1, 3}

So the correct response is:
**{0, 1, 3}**.