Answer :
Let's break down each of the given choices to understand which event corresponds to exactly one outcome of rolling a six-sided die.
### Choice Analysis:
A. Both numbers are 5s.
- When rolling two six-sided dice, the event "both numbers are 5s" means that the first die must show 5 and the second die must also show 5.
- There is only one specific outcome (5, 5) that satisfies this condition.
B. Neither number is a 5.
- If neither number is a 5, it means both dice must show numbers other than 5.
- We have several possible outcomes here, including (1, 1), (1, 2), (1, 3), (1, 4), (1, 6), and similarly for all combinations that do not include the number 5.
- This results in multiple possible outcomes.
C. The sum of the numbers is 3.
- For the sum of the numbers to be 3, we can have the following outcomes: (1, 2) or (2, 1).
- This gives us more than one possible outcome.
D. One of the numbers is a 3.
- If one of the dice shows a 3, possible outcomes include (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), and similarly (1, 3), (2, 3), (4, 3), (5, 3), (6, 3).
- This results in multiple possible outcomes.
### Conclusion:
The only event that corresponds to exactly one specific outcome is "Both numbers are 5s," which matches Choice A.
Therefore, the correct answer is:
A. Both numbers are 5s.
### Choice Analysis:
A. Both numbers are 5s.
- When rolling two six-sided dice, the event "both numbers are 5s" means that the first die must show 5 and the second die must also show 5.
- There is only one specific outcome (5, 5) that satisfies this condition.
B. Neither number is a 5.
- If neither number is a 5, it means both dice must show numbers other than 5.
- We have several possible outcomes here, including (1, 1), (1, 2), (1, 3), (1, 4), (1, 6), and similarly for all combinations that do not include the number 5.
- This results in multiple possible outcomes.
C. The sum of the numbers is 3.
- For the sum of the numbers to be 3, we can have the following outcomes: (1, 2) or (2, 1).
- This gives us more than one possible outcome.
D. One of the numbers is a 3.
- If one of the dice shows a 3, possible outcomes include (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), and similarly (1, 3), (2, 3), (4, 3), (5, 3), (6, 3).
- This results in multiple possible outcomes.
### Conclusion:
The only event that corresponds to exactly one specific outcome is "Both numbers are 5s," which matches Choice A.
Therefore, the correct answer is:
A. Both numbers are 5s.
