To solve the problem of finding the probability that a randomly selected letter from the English alphabet comes after the letter [tex]$D$[/tex], let's go through the process step-by-step.
1. Total Number of Letters: The English alphabet contains a total of 26 letters.
2. Identifying Letters After [tex]$D$[/tex]:
- The letter [tex]$D$[/tex] is the 4th letter in the alphabet.
- The letters that come after [tex]$D$[/tex] are [tex]$E, F, G, ..., Z$[/tex].
- Thus, the letters after [tex]$D$[/tex] start from position 5 onwards.
3. Counting the Letters After [tex]$D$[/tex]:
- If we subtract the 4 letters (A, B, C, D) that come before and including [tex]$D$[/tex] from the total number of letters, we get the number of letters after [tex]$D$[/tex].
- So, the number of letters after [tex]$D$[/tex] is [tex]\(26 - 4 = 22\)[/tex].
4. Calculating the Probability:
- Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
- Here, the favorable outcomes are the 22 letters that come after [tex]$D$[/tex].
- Therefore, the probability is [tex]\(\frac{22}{26}\)[/tex].
5. Simplifying the Fraction:
- [tex]\(\frac{22}{26}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
- Simplifying [tex]\(\frac{22}{26}\)[/tex] gives [tex]\(\frac{11}{13}\)[/tex].
Therefore, the probability that a randomly selected letter from the English alphabet comes after [tex]$D$[/tex] is [tex]\(\frac{11}{13}\)[/tex].
So, the correct answer is:
B. [tex]\(\frac{11}{13}\)[/tex]
