UPSC NDA Math Model Paper 2

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=

n(A)

N

=

15

36

=

5

12

.