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.

On drawing a card from the box,

Sample space = {a, b, c, ……, m, n, o, p}.

(i) Let E₁ be the event of drawing a vowel card.

E₁ = {a, e, i, o}

∴ The number of favourable outcomes to the event E₁ = 4.

$\therefore P(E$1) = \dfrac{\text{No. of favourable outcomes to } E1}{\text{Total no. of possible outcomes}} = \dfrac{4}{16} = \dfrac{1}{4}.

Hence, the probability of drawing a vowel card is $\dfrac{1}{4}$.

(ii) Let E₂ be the event of drawing a consonant card.

Since, there are 4 vowels in the range a, b, ….., p. Hence, no. of consonants = 16 - 4 = 12.

∴ The number of favourable outcomes to the event E₂ = 12.

$\therefore P(E$2) = \dfrac{\text{No. of favourable outcomes to } E2}{\text{Total no. of possible outcomes}} = \dfrac{12}{16} = \dfrac{3}{4}.

Hence, the probability of drawing a consonant card is $\dfrac{3}{4}$.

(iii) Let E₃ be the event of drawing a card not containing letters of word median.

Since, there are 6 letters in the word median. Hence, no. of other letters = 16 - 6 = 10.

∴ The number of favourable outcomes to the event E₃ = 10.

$\therefore P(E$3) = \dfrac{\text{No. of favourable outcomes to } E3}{\text{Total no. of possible outcomes}} = \dfrac{10}{16}= \dfrac{5}{8}.

Hence, the probability of drawing a card not containing letters of word 'median' is $\dfrac{5}{8}$.