Question

Two dice are thrown, find the probability of getting
(1) The sum of numbers on their upper faces is at least 10.
(2) The sum of the numbers on their upper faces is divisible by 5.
(3) The number on the upper face of the first die is greater than the number on the upper face of the second die.

Answer 1

Two dice are thrown
$\therefore$ Sample space = S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4),  (2, 5), (2, 6), (3, 1),(3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2),(5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
$\therefore$
(1) A = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}
  n(A) = 6

Probability, P(A) = `"n(A)"/"n(S)" = 6/36 = 1/6`

(2) $B=\{(1,4),(2,3),(3,2),(4,1),(4,6),(5,5),(6,4)\}$

Probability, P(B) = `"n(B)"/"n(S)" = 7/36`

(3) $C=\{(2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(5,4),(6,1),(6,2),(6,3),(6,4),(6,5)\}$

Probability, P(C) = `"n(C)"/"n(S)" = 15/36`