Answer :
To determine which event will have a sample space of [tex]\( S = \{A, B, C\} \)[/tex], let's analyze each option provided step-by-step:
1. Flipping a fair, two-sided coin:
- In this event, the coin has two sides, typically labeled "Heads" and "Tails."
- Therefore, the sample space for this event is [tex]\(\{ \text{Heads}, \text{Tails} \}\)[/tex].
- This does not match the given sample space [tex]\( S = \{A, B, C\} \)[/tex].
2. Rolling a six-sided die:
- A standard six-sided die has faces numbered 1 through 6.
- Thus, the sample space for rolling the die is [tex]\(\{1, 2, 3, 4, 5, 6\}\)[/tex].
- This also does not match the given sample space [tex]\( S = \{A, B, C\} \)[/tex].
3. Spinning a spinner with three sections labeled [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex]:
- In this event, the spinner is divided into three sections, each labeled with one of the letters [tex]\( A \)[/tex], [tex]\( B \)[/tex], or [tex]\( C \)[/tex].
- Therefore, the sample space for this event is [tex]\(\{A, B, C\}\)[/tex].
- This perfectly matches the given sample space [tex]\( S = \{A, B, C\} \)[/tex].
4. Choosing a tile from a pair of tiles, one with the letter [tex]\( A \)[/tex] and one with the letter [tex]\( B \)[/tex]:
- In this event, there are only two tiles available, one labeled [tex]\( A \)[/tex] and one labeled [tex]\( B \)[/tex].
- The sample space for this event is [tex]\(\{A, B\}\)[/tex].
- This does not match the given sample space [tex]\( S = \{A, B, C\} \)[/tex].
After analyzing each option, we find that the event that will have a sample space of [tex]\( S = \{A, B, C\} \)[/tex] is:
Spinning a spinner with three sections labeled [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex].
1. Flipping a fair, two-sided coin:
- In this event, the coin has two sides, typically labeled "Heads" and "Tails."
- Therefore, the sample space for this event is [tex]\(\{ \text{Heads}, \text{Tails} \}\)[/tex].
- This does not match the given sample space [tex]\( S = \{A, B, C\} \)[/tex].
2. Rolling a six-sided die:
- A standard six-sided die has faces numbered 1 through 6.
- Thus, the sample space for rolling the die is [tex]\(\{1, 2, 3, 4, 5, 6\}\)[/tex].
- This also does not match the given sample space [tex]\( S = \{A, B, C\} \)[/tex].
3. Spinning a spinner with three sections labeled [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex]:
- In this event, the spinner is divided into three sections, each labeled with one of the letters [tex]\( A \)[/tex], [tex]\( B \)[/tex], or [tex]\( C \)[/tex].
- Therefore, the sample space for this event is [tex]\(\{A, B, C\}\)[/tex].
- This perfectly matches the given sample space [tex]\( S = \{A, B, C\} \)[/tex].
4. Choosing a tile from a pair of tiles, one with the letter [tex]\( A \)[/tex] and one with the letter [tex]\( B \)[/tex]:
- In this event, there are only two tiles available, one labeled [tex]\( A \)[/tex] and one labeled [tex]\( B \)[/tex].
- The sample space for this event is [tex]\(\{A, B\}\)[/tex].
- This does not match the given sample space [tex]\( S = \{A, B, C\} \)[/tex].
After analyzing each option, we find that the event that will have a sample space of [tex]\( S = \{A, B, C\} \)[/tex] is:
Spinning a spinner with three sections labeled [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex].
