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”

Given,

Sample space S = {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}

Total number of outcomes = 16

(i) Let A be the event of getting a vowel, then

A = {a, e, i, o}

∴ The number of favourable outcomes to the event A = 4

∴ P(A) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{4}{16} = \dfrac{1}{4}$

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

(ii) Let B be the event of getting a consonant, then

B = {b, c, d, f, g, h, j, k, l, m, n, p}

∴ The number of favourable outcomes to the event B = 12

∴ P(B) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{12}{16} = \dfrac{3}{4}$

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

(iii) Let C be the event of not getting letters of word median, then

C = {b, c, f, g, h, j, k, l, o, p}

∴ The number of favourable outcomes to the event C = 10

∴ P(C) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{10}{16} = \dfrac{5}{8}$

Hence, the probability of not getting letters of word median is $\dfrac{5}{8}$.