(i) ∵ Letter is selected at random from the alphabet.
∴ Possible outcomes = n(S) = 26C1 = 26.
Let event E1 be event that selected letter is one of the letters in the word probability.
∴ Number of favourable outcomes to event E1 = n(E1) = 9C1 = 9.
(∵ Total different letters in word probability is 9)
(p, r, o, b, a, i, l, t, y)
∴ P(E1) = \(\frac{n(E_1)}{n(S)}\) = 9/26.
(ii) Let event E2 be event that selected letter occurs in the first half of the alphabet.
∴ n(E2) = 13
∴ P(E2) = \(\frac{n(E_2)}{n(S)}\) = 13/26 = 1/2
(iii) Let event E3 be event that selected letter is a letter after x.
∴ n(E3) = 2
∴ P(E3) = \(\frac{n(E_3)}{n(S)}\) = 2/26 = 1/13.