Each of the letter of the word 'BOUNDARIES' is written on identical cards and put in the bag. they are shuffled if a card is drawn at random, What is the probability that the letter is

(i) a consonant

(ii) one of the letter of the word 'LUCKNOW' ?

(iii) one of the letter of the word 'INDIA' ?

(i) No. of consonants in the word 'BOUNDARIES' = 5 [B, N, D, R, S]

∴ No. of favourable outcomes = 5

Total no. of letters in the word 'BOUNDARIES' = 10.

∴ No. of possible outcomes = 10

P(that card drawn has a consonant) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{5}{10} = \dfrac{1}{2}$

Hence, probability of getting a consonant = $\dfrac{1}{2}$.

(ii) No. of different letters in the word 'LUCKNOW' that are also present in the word 'BOUNDARIES'` = 3 (U, N, O)

∴ No. of favourable outcomes = 3

P(that the letter on card is a letter of the word 'LUCKNOW') = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{10}$

Hence, probability of getting one of the letter of the word 'LUCKNOW' = $\dfrac{3}{10}$.

(iii) No. of different letters in the word 'INDIA' that are also present in the word 'BOUNDARIES'` = 4 (I, N, D, A)

∴ No. of favourable outcomes = 4

P(that the letter on card is a letter of the word 'INDIA') = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{4}{10} = \dfrac{2}{5}$

Hence, probability of getting one of the letter of the word 'INDIA' = $\dfrac{2}{5}$.