Question

Each letter of the word “INDEPENDENT” is written on individual cards. The cards are placed in a box and mingled thoroughly. A card with letter ‘N’ is removed from the box. Now find the probability of picking a card with a consonant?

(a) \(\frac 7{11}\)

(b) \(\frac 7{10}\)

(c) \(\frac 35\)

(d) \(\frac 25\)

Answer 1

Correct option is (c) \(\frac 35\)

The total number of letters in the word INDEPENDENT is 11.

Out of them 4 are vowels and the rest are (11 - 4) = 7 are consonants.

N, which is a consonant, is removed.

∴ the number of the letters or the probability space = 11 - 1 = 10

and the number of consonants or the favourable events = 7 - 1 = 6.

∴ P(consonant) = \(\frac{\text{Number of favourable events}}{\text{Probabilty space}}\)

\(=\frac 6 {10}\)

\(= \frac 35\)