Two dice are thrown. Find the probability of the following events :(a) Event A : The sum of the numbers on their upper faces is at least 9.(b) Event B : The sum of the numbers on their upper faces is divisible by 5.(c) Event C : The number on the upp…

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

Two dice are thrown, so \(n(S) = 6 \times 6 = 36\).

(a) Sum at least 9 means sum 9, 10, 11 or 12: (3,6), (4,5), (5,4), (6,3); (4,6), (5,5), (6,4); (5,6), (6,5); (6,6) — 10 outcomes. \(P(A) = \dfrac{10}{36} = \dfrac{5}{18}\).

(b) Sum divisible by 5 means sum 5 or 10: (1,4), (2,3), (3,2), (4,1); (4,6), (5,5), (6,4) — 7 outcomes. \(P(B) = \dfrac{7}{36}\).

(c) First number greater than the second: 15 outcomes (5 + 4 + 3 + 2 + 1). \(P(C) = \dfrac{15}{36} = \dfrac{5}{12}\).