Question

What is the probability of getting a sum of 7 on two rolls of a die?

• A. $\frac{7}{12}$
• B. $\frac{1}{11}$
• C. $\frac{1}{6}$
• D. $\frac{2}{3}$

Answer 1

The correct option is C

$\frac{1}{6}$

The total possible outcomes when a die is rolled twice are:

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

Total number of outcomes = 36

Number of ways to get sum as 7 = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

= 6

$P\left(\text{getting sum as 7}\right)=\frac{\text{Favourable outcomes}}{\text{Total possible outcomes}}$

$=\frac{Outcomehavingsamenumbers}{TotalOutcomes}$

$=\frac{6}{36}$

= $\frac{1}{6}$