If four consecutive letters are selected at random from the English alphabet,…

Answer: 17/23

Reasoning:

1) Total number of ways to pick four consecutive letters from the 26-letter English alphabet:

There are 26 - 4 + 1 = 23 possible consecutive 4-letter blocks (e.g., abcd, bcde, ..., wxyz).

2) Count the blocks that contain no vowels (only consonants):

• The vowels are a, e, i, o, u. The longest runs of consecutive consonants occur between vowels: j–n (jklmn), p–t (pqrst), and v–z (vwxyz).

• Each run of 5 consonants yields 5 - 4 + 1 = 2 distinct 4-letter consonant-only blocks.

• The specific all-consonant 4-letter blocks are: jklm, klmn, pqrs, qrst, vwxy, wxyz (6 blocks total).

3) Compute the required probability:

Number of blocks containing at least one vowel = total blocks − consonant-only blocks = 23 − 6 = 17.

Therefore the probability that a randomly selected consecutive 4-letter block contains at least one vowel is 17/23.