Sixteen cards are labelled as a, b, c, ………., m, n, o, p. They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card drawn is :

(i) a vowel

(ii) a consonant

(iii) none of the letters of the word median ?

No. of possible outcomes = 16.

(i) Vowels between a, b, c, ………., m, n, o, p are a, e, i, o.

∴ No. of favourable outcomes = 4.

P(that the card drawn is a vowel)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{4}{16} = \dfrac{1}{4}$.

Hence, the probability that the card drawn is a vowel = $\dfrac{1}{4}$.

(ii) Since, there are 4 vowels.

∴ No. of consonants or favourable outcomes = 12 (16 - 4).

P(that the card drawn is a consonant)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{12}{16} = \dfrac{3}{4}$.

Hence, the probability that the card drawn is a consonant = $\dfrac{3}{4}$.

(iii) Letters of the word median are 'm', 'e', 'd', 'i', 'a' and 'n'.

No. of letters left = 16 - 6 = 10.

∴ No. of favourable outcomes = 10.

P(that the card contains none of the letters of the word median)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{10}{16} = \dfrac{5}{8}$.

Hence, the probability that the card drawn contains none of the letters of the word median = $\dfrac{5}{8}$.