What is the probability of rolling a sum equal to a prime number when rolling a pair of dice, expressed in simplest fractional form?

To find the probability of rolling a sum equal to a prime number with a pair of dice, we first identify the possible sums and then determine which sums are prime.

When rolling two six-sided dice, the possible sums range from 2 (1+1) to 12 (6+6). The sums that can be obtained are:

• 2

• 3

• 4

• 5

• 6

• 7

• 8

• 9

• 10

• 11

• 12

Next, we identify which of these sums are prime numbers. A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself. The prime sums from our list are:

• 2 (not a valid case here as it cannot be obtained by rolling two dice)

• 3 (can be rolled as 1+2 or 2+1)

• 5 (can be rolled as 1+4, 2+3, or 3+2, or 4+1)

• 7 (can be rolled as 1+6, 2+5, 3+4, 4+