Question

Two dice are thrown at the same time. Find the probability that the sum of numbers appearing is a prime.

• A. $\frac{7}{36}$
• B. $\frac{7}{18}$
• C. $\frac{5}{18}$
• D. $\frac{5}{12}$

Answer 1

The correct option is D

$\frac{5}{12}$

The total possible outcomes when two dice are rolled 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 a prime number {i.e.,2, 3, 5, 7, 11} = {(1,1), (1,2), (2,1), (2,3), (3,2), (4,1), (1,4), (3,4), (4,3), (2,5), (5,2), (6,1), (1,6), (5,6), (6,5)}

$=15$

P(getting sum prime numbers)
$=\frac{\text{Favourable outcomes}}{\text{Total possible outcomes}}$

$=\frac{\text{Outcome as the sum as a prime number}}{\text{Total Outcome}}$

$=\frac{15}{36}$

$=\frac{5}{12}$