An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice in succession and the number on the top face is recorded each time. The probability that the sum of the two recorded numbers is a prime number is ________

When an unbiased six-faced die is rolled twice in succession, the total number of possible outcomes in the sample space is:

The possible sums of the two recorded numbers range from $1 + 1 = 2$ to $6 + 6 = 12$.

The prime numbers in the range $[2, 12]$ are $2, 3, 5, 7,$ and $11$.

Let us list all favorable outcomes for each prime sum:

• Sum = 2: $(1, 1) \implies 1$ outcome

• Sum = 3: $(1, 2), (2, 1) \implies 2$ outcomes

• Sum = 5: $(1, 4), (2, 3), (3, 2), (4, 1) \implies 4$ outcomes

• Sum = 7: $(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) \implies 6$ outcomes

• Sum = 11: $(5, 6), (6, 5) \implies 2$ outcomes

Total number of favorable outcomes:

Therefore, the required probability is:

Hence, option (C) is the correct answer.