The letters A, D, M, N, O, S, U and 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:
(a) of the word MONDAY?
(b) which does not appear in MONDAY?
(c) which appears both in SUNDAY and MONDAY?
The cards contain {A, D, M, N, O, S, U, Y}.
Total number of cards = 8.
(a) The letters of MONDAY present on the cards are {M, O, N, D, A, Y}.
Number of favourable cards = 6.
Required probability = \frac{6}{8}
⇒ Required probability = \frac{3}{4}
(b) The cards whose letters do not appear in MONDAY are {S, U}.
Number of favourable cards = 2.
Required probability = \frac{2}{8}
⇒ Required probability = \frac{1}{4}
(c) The letters that appear in both SUNDAY and MONDAY are {N, D, A, Y}.
Number of favourable cards = 4.
Required probability = \frac{4}{8}
⇒ Required probability = \frac{1}{2}
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