Question

A letter is chosen at random from the word ‘ASSASSINATION’. Find the probability that letter is
(i) a vowel (ii) an consonant

Answer 1

There are 13 Letters in the word ASSASSINATION Which contains 6 vowels and 7 consonants.
One letter is selected out of 13 letters in ${}^{13}{C}_1=13\text{ways}$
(i) One vowel is selected out of 6 vowels in
${}^6{C}_1=6$
Thus probability of a vowel $=\frac{6}{13}$
(ii) One consonant is selected out of 7 consonant in
${}^7{C}_1=7\text{ways}$
Thus probability of a consonant $=\frac{7}{13}$