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?

A. {2,6}
B. {0,1,3}
C. {1,2,3,4,5,6,7,8,9,10}
D. {2,4,5,6,7,8,9,10}

Answer 1

To determine the complement of the set of pins that Sam and Silvie knocked down in the bowling game, we first need to identify all of the unique scores (total pins knocked down) recorded by both players.

From the given scores:
- Sam: 5, 6, 7, 8, 10, 9, 4, 10, 4, 6
- Silvie: 8, 5, 7, 5, 2, 9, 10, 4, 5, 9

Firstly, let's combine all the scores from both players:
- Sam's scores: 5, 6, 7, 8, 10, 9, 4
- Silvie's scores: 8, 5, 7, 5, 2, 9, 10, 4, 5, 9

Now let's list all the unique pins knocked down by both Sam and Silvie:
- From Sam: {4, 5, 6, 7, 8, 9, 10}
- From Silvie: {2, 4, 5, 7, 8, 9, 10}

The unique pins knocked down can thus be combined into one set:
- Unique set: {2, 4, 5, 6, 7, 8, 9, 10}

The sample space for the total pins that can be knocked down in one frame (considering the game of bowling) would be:
- Sample space: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

The complement of the set of pins knocked down by Sam and Silvie would include all the numbers in the sample space that were not knocked down by either player.

Now, let’s determine the complement:
- Pins knocked down: {2, 4, 5, 6, 7, 8, 9, 10}
- Complement (in the sample space) would be all numbers NOT in the knocked down set: {0, 1, 3}

Now let's evaluate the options:
A. {2, 6} - Not the complement, as both 2 and 6 were knocked down.
B. {0, 1, 3} - Correct, as these are not in the knocked down set.
C. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} - Not the complement, many of these were knocked down.
D. {2, 4, 5, 6, 7, 8, 9, 10} - Not the complement, these are the pins knocked down.

Thus, the correct answer is:

**B. {0, 1, 3}**