Question

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is

• A. $\frac{1}{4}$
• B. $\frac{5}{36}$
• C. $\frac{5}{12}$
• D. $\frac{5}{6}$

Answer 1

The correct option is C $\frac{5}{12}$

The possible sums are $2,3,5,7,11$.
The combinations whose sum is a prime number are : $(1,1),(1,2),(2,1),(2,3),(3,2),(1,4),(4,1),(3,4),(4,3),(6,1),(1,6),(2,5),(5,2),(5,6),(6,5)$
Total Number of combinations $=6\times 6=36$
The required probability $=\frac{15}{36}$