Concept:

The probability of the occurrence of an event A out of a total possible outcomes N, is given by: \(P(A) = \rm \dfrac{n(A)}{N}\), where n(A) is the number of ways in which the event A can occur.

Calculation:

The total number of distinct possible outcomes (N), when rolling two dice, are: N = 6 × 6 = 36.

The sum of these pairs of outcomes can be a number from 1 + 1 = 2 to 6 + 6 = 12.

The prime numbers from 2 to 12 are (2, 3, 5, 7, 11). The different possibilities to give each of these sums are given below:

Sum = 2:

(1, 1) = 1 possibility.

Sum = 3:

(1, 2), (2, 1) = 2 possibilities.

Sum = 5:

(1, 4), (4, 1), (2, 3), (3, 2) = 4 possibilities.

Sum = 7:

(1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3) = 6 possibilities.

Sum = 11:

(5, 6), (6, 5) = 2 possibilities.

Total Number of possibilities for the desired event to occur is: n(A) = 1 + 2 + 4 + 6 + 2 = 15.

The required probability is therefore: \(P = \rm \dfrac{n(A)}{N}=\dfrac{15}{36}=\dfrac{5}{12}\).

The following table gives the number of ways in which a given sum can be obtained when rolling a pair of dice:

The number 7 has the maximum number of possibilities.