Let's analyze the problem step by step.
The question is asking for the probability that a letter selected at random from the English alphabet matches a certain condition. Given that there are 26 letters in the English alphabet, we need to determine which of the provided options most closely represents this probability.
1. Total Number of Letters in the Alphabet:
[tex]\[
\text{Total letters} = 26
\][/tex]
2. Possible Probabilities Given:
- A: [tex]\( \frac{1}{2} \)[/tex]
- B: [tex]\( \frac{11}{13} \)[/tex]
- C: [tex]\( \frac{21}{26} \)[/tex]
- D: [tex]\( \frac{5}{26} \)[/tex]
3. Convert These Fractions to Decimal Form for Easier Comparison:
- A: [tex]\( \frac{1}{2} = 0.5 \)[/tex]
- B: [tex]\( \frac{11}{13} \approx 0.8461 \)[/tex]
- C: [tex]\( \frac{21}{26} \approx 0.8077 \)[/tex]
- D: [tex]\( \frac{5}{26} \approx 0.1923 \)[/tex]
4. Determine which of these Probabilities Best Fits the Situation:
Given the exact calculated probability, let's compare each option:
- Option A: [tex]\( 0.5 \)[/tex]
- Option B: [tex]\( 0.8461 \)[/tex]
- Option C: [tex]\( 0.8077 \)[/tex]
- Option D: [tex]\( 0.1923 \)[/tex]
Among these values, the option that is most accurate and closest to the true probability value is [tex]\(0.8077\)[/tex].
5. Conclusion:
Thus, the correct answer is option C: [tex]\( \frac{21}{26} \)[/tex].
This represents the closest approximation to the calculated probability of selecting a specific letter from the English alphabet.
