Asked in: July 2025 board paper; July 2024 board paper (3 marks: two dice, sum a multiple of 5, and sum 25 which is an impossible event, P = 0)Q.12 Two dice are thrown. Find the probability of the following events:(a) Event A: The sum of the numbers…

Answer: \(P(A) = \dfrac{5}{18}\), \(P(B) = \dfrac{7}{36}\), \(P(C) = \dfrac{5}{12}\)

S = {(1,1), (1,2), …, (6,6)}, all 36 ordered pairs, n(S) = 36.

(a) Sum at least 9 means sum = 9, 10, 11 or 12.

A = {(3,6), (4,5), (5,4), (6,3), (4,6), (5,5), (6,4), (5,6), (6,5), (6,6)}, n(A) = 10

\(P(A) = \dfrac{10}{36} = \dfrac{5}{18}\)

(b) Sum divisible by 5 means sum = 5 or 10.

B = {(1,4), (2,3), (3,2), (4,1), (4,6), (5,5), (6,4)}, n(B) = 7

\(P(B) = \dfrac{7}{36}\)

(c) First number greater than second:

C = {(2,1), (3,1), (3,2), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3), (5,4), (6,1), (6,2), (6,3), (6,4), (6,5)}, n(C) = 15

\(P(C) = \dfrac{15}{36} = \dfrac{5}{12}\)