The following letters A, D, M, N, O, S, U, Y of the English alphabet are written on separate cards and put in a box. The cards are well shuffled and one card is drawn at random. What is the probability that the card drawn is a letter of the word,
(a) MONDAY?
(b) which does not appear in MONDAY?
(c) which appears both in SUNDAY and MONDAY?
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Letters written on cards = {'A', 'D', 'M', 'N', 'O', 'S', 'U', 'Y'}
No. of cards = 8
(a) Letters of the word MONDAY present in the cards = {'M', 'O', 'N', 'D', 'A', 'Y'}
Probability that the card drawn is a letter of the word MONDAY
= $\frac{\text{Letters of MONDAY present}}{\text{No. of cards}} = \frac{6}{8} = \frac{3}{4}$.
Hence, required probability = $\frac{3}{4}$.
(b) Letters of the word not present in MONDAY = {'S', 'U'}
Probability that the card drawn is not a letter of the word MONDAY
= $\frac{\text{Letters not present in MONDAY}}{\text{No. of cards}} = \frac{2}{8} = \frac{1}{4}$.
Hence, required probability = $\frac{1}{4}$.
(c) Letters of the word present in SUNDAY and MONDAY are {'N', 'D', 'A', 'Y'}.
Probability that the card drawn has a letter which appears both in SUNDAY and MONDAY
= $\frac{\text{Letters present in both MONDAY and SUNDAY}}{\text{No. of cards}} = \frac{4}{8} = \frac{1}{2}$.
Hence, required probability = $\frac{1}{2}$.