Question

Two dice are rolled. Find the probability that the sum of the digits on the upper face is 7.

• A. $\frac{4}{6}$
• B. $\frac{1}{2}$
• C. $\frac{1}{6}$
• D. $\frac{1}{3}$

Answer 1

The correct option is C $\frac{1}{6}$

Number of elements in sample space = 6$\times$ 6 =36

	1	2	3	4	5	6
1	(1,1)	(1,2)	(1,3)	(1,4)	(1,5)	(1,6)
2	(2,1)	(2,2)	(2,3)	(2,4)	(2,5)	(2,6)
3	(3,1)	(3,2)	(3,3)	(3,4)	(3,5)	(3,6)
4	(4,1)	(4,2)	(4,3)	(4,4)	(4,5)	(4,6)
5	(5,1)	(5,2)	(5,3)	(5,4)	(5,5)	(5,6)
6	(6,1)	(6,2)	(6,3)	(6,4)	(6,5)	(6,6)

$Probability=\frac{Favourablenumberofoutcomes}{Totalnumberofoutcomes}$
Favourable outcomes = (1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3)
No. of favorable outcomes = 6
Let the given event is A.
$\therefore$ P(A) = $\frac{6}{36}$ = $\frac{1}{6}$