Question

If a letter is chosen at random from the English alphabet, find the probability that the letter is

(i) a vowel

(ii) a consonant

Answer 1

As the better is choosen from English alphabet
$\therefore n\left(S\right)=26$

[$\because$ There am 26 letters in English alphabet]

(i) Let E be the event that a vowel has been choosen

$\therefore n\left(E\right){=}^5{C}_1$

($\because$ There are h vowels in English alphabet]

$\therefore P\left(E\right)=\frac{5}{26}$

(ii) Probability that a consonant is choosen

$\Rightarrow P\left(\overline{E}\right)=1-P\left(E\right)$

$=1-\frac{5}{26}=\frac{21}{26}$