Question

Two dice are thrown. Find the probability of the events.

(ii) The sum of the numbers on their upper faces is multiple of 7.

Answer 1

Given:
Two dice are thrown.
The sample space is {(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)}.
∴ n(S) = 36
Now,
Let Y be the event that the sum of the numbers on the upper faces of the dice is a multiple of 7.
∴ Y = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}
Or,
n(Y) = 6
Thus, we have:
P(Y) = $\frac{n\left(Y\right)}{n\left(S\right)}=\frac{6}{36}=\frac{1}{6}$