Arnav rolls two dice simultaneously. What is the probability of Arnav getting two numbers whose sum is a prime number?
Answer & explanation
Correct answer: option 1
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:
$\frac{15}{36} = \frac{5}{12}$