Arnav rolls two dice simultaneously. What is the probability of Arnav getting two numbers whose sum is a prime number?

$\frac{5}{12}$

The correct answer is Option (1) → $\frac{5}{12}$

When two fair dice are rolled, the total number of possible outcomes is:

$6 \times 6 = 36$

Prime numbers possible as the sum of two dice:

Prime sums between 2 and 12 are:

$2,\ 3,\ 5,\ 7,\ 11$

Count favorable outcomes:

• Sum = 2 → (1,1) → 1 way
• Sum = 3 → (1,2), (2,1) → 2 ways
• Sum = 5 → (1,4), (2,3), (3,2), (4,1) → 4 ways
• Sum = 7 → (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 ways
• Sum = 11 → (5,6), (6,5) → 2 ways

Total favorable outcomes =

$1 + 2 + 4 + 6 + 2 = 15$

Probability:

$\frac{15}{36} = \frac{5}{12}$