Question

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,

1. MONDAY?
2. Which does not appear in MONDAY?
3. Which appears both in SUNDAY and MONDAY?

Answer 1

Total outcomes n(s) = 8

a. Favourable outcomes, n(E) = 6

`P(E) = (n(E))/(n(S))`

= `6/8`

= `3/4`

b. `P(barE) = 1 - P(E)`

= `1 - 3/4`

= `(4 - 3)/4`

= `1/4`

c. Favourable outcomes = uncommon letters

= N, D, A, Y

= 4

Then, required probability = `4/8 = 1/2`