A letter is selected at random from the alphabet. What is the probability that it is one of the letters in the word "probability?" What is the probability that it occurs in the first half of the alphabet? What is the probability that it is a letter after \( x \) ?

Question

A letter is selected at random from the alphabet. What is the probability that it is one of the letters in the word "probability?" What is the probability that it occurs in the first half of the alphabet? What is the probability that it is a letter after \( x \) ?

Answer 1

(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.

Comments

Thanks the answers are correct.