Model Answer
0 min readIntroduction
The statement "Either of the five dancers will dance tonight" presents a scenario of definite occurrence within a limited set of possibilities. This isn’t a question of probability in the traditional sense, but rather a statement of certainty. It implies that one, and only one, of the five dancers *will* perform. This understanding is crucial for correctly interpreting the statement and providing a clear and concise response. The question tests the ability to discern logical certainty from potential probabilistic outcomes.
The statement "Either of the five dancers will dance tonight" signifies a guaranteed event. It doesn't imply a 50% chance for each dancer, nor does it suggest any uncertainty about whether *someone* will dance. Instead, it establishes a condition where one of the five dancers is definitively scheduled to perform.
Understanding the Logic
The key word here is "either." In this context, "either...or" implies a mutually exclusive choice. This means only one of the five dancers will dance, and the statement guarantees that *someone* will dance. It’s a deterministic statement, not a probabilistic one.
Breaking Down the Possibilities
Let's represent the dancers as D1, D2, D3, D4, and D5. The statement means:
- D1 will dance, OR
- D2 will dance, OR
- D3 will dance, OR
- D4 will dance, OR
- D5 will dance.
But only one of these can be true. The statement assures us that one of these options *must* be true.
Distinguishing from Probability
It’s important to differentiate this from a scenario where we might say, "One of the five dancers *might* dance." The use of "will" establishes certainty. If the statement were phrased differently, such as "There is a possibility that one of the five dancers will dance," then it would introduce an element of probability. However, the current phrasing removes that ambiguity.
Illustrative Example
Imagine a dance competition where only one dancer is selected to perform each night. The organizer announces, "Either of the five finalists will dance tonight." This announcement doesn't mean each finalist has a 20% chance of dancing. It means the organizer has already chosen one of the five, and that dancer *will* perform. The selection is already made, even if the audience doesn't know which dancer it is.
Formal Logical Representation
The statement can be represented logically as: (D1 ∨ D2 ∨ D3 ∨ D4 ∨ D5) ∧ ¬(D1 ∧ D2 ∧ D3 ∧ D4 ∧ D5). This means that at least one of the dancers will dance, and it is not possible for all of them to dance simultaneously.
Conclusion
In conclusion, the statement "Either of the five dancers will dance tonight" is a declaration of certainty, not probability. It guarantees that one, and only one, of the five dancers will perform. Understanding the logical implication of the word "either" and the use of "will" is crucial to correctly interpreting the statement. The statement establishes a definite outcome within a defined set of possibilities, removing any ambiguity about whether a performance will occur.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.