A letter of english alphabets is chosen at random.

We know that, in english alphabets, there are (5 vowels + 21 consonants)=26 letters. So,

total number of outcomes in english alphabets are,                                                                                               

n(S) = 26

Let $E=$ Event of choosing a english alphabet, which is a consonent

$=\{b, c, d, t, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z\}$

$\therefore \quad n(E)=21$

Hence, required probability $=\frac{n(E)}{n(S)}=\frac{21}{26}$