Question

When two dice are thrown , the probability of getting a sum of 6 is ___________

• A. $\frac{1}{36}$
• B. $\frac{5}{12}$
• C. $\frac{5}{36}$
• D. $\frac{1}{3}$

Answer 1

The correct option is C

$\frac{5}{36}$

Let us make a table to show all possible outcomes

$$\begin{array}{ccccccc}& \text{1}& \text{2}& \text{3}& \text{4}& \text{5}& \text{6}\\ 1& 1,1& 1,2& 1,3& 1,4& 1,5& 1,6\\ 2& 2,1& 2,2& 2,3& 2,4& 2,5& 2,6\\ 3& 3,1& 3,2& 3,3& 3,4& 3,5& 3,6\\ 4& 4,1& 4,2& 4,3& 4,4& 4,5& 4,6\\ 5& 5,1& 5,2& 5,3& 5,4& 5,5& 5,6\\ 6& 6,1& 6,2& 6,3& 6,4& 6,5& 6,6\end{array}$$

$\therefore$ Total number of outcomes when two dice are thrown simultaneously, is =36

The favourable outcome, in this case, is (1, 5), (5,1 ) , (2,4), (4,2 ) , (3,3) = 5 favourable outcomes

Hence the probability of getting a sum of 12 when two dice are thrown simultaneously is
= $\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$
= $\frac{5}{36}$