Question

Two dice are thrown simultaneously. What is the probability of getting two numbers whose sum is 10?
(a) $\frac{5}{18}$
(b) $\frac{1}{6}$
(c) $\frac{1}{12}$
(d) $\frac{1}{4}$

Answer 1

(c) $\frac{1}{12}$

Explanation:
When two dice are thrown simultaneously, all possible outcomes are:
(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)
Number of all possible outcomes = 36

Let E be the event that the sum of the numbers appearing on the top of the two dice is equal to 10.
Then the favourable outcomes are:
(4,6), (6,4), (5,5)
Number of favourable outcomes = 3
∴ P( getting a sum equal to 10) = $\frac{3}{36}=\frac{1}{12}$