UPSC NDA 2 2019 Mathematics Solved Paper

When two dice are thrown
Then, Sample space
S = {(1, 1), (1, 2), ..., (1, 6), (2, 1, (2, 2), ..., (2, 6), (3, 1), (3, 2), ..., (3, 6), (4, 1), (4, 2), ..., (4, 6), (5, 1), (5, 2), ..., (5, 6), (6, 1), (6, 2), ..., (6, 6)}
∴S=36
Let A be the event getting the sum as a prime number i.e., 2, 3, 5, 7, 11 as the sum
Then, A = {(1, 1), (1, 2), (2, 1), (1, 4), (4, 1), (2, 3), (3, 2), (1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3), (6, 5), (5, 6)}
Favourable number of elementary events = 15
i.e., n(A)=15
So, the required probability =

15

36

=

5

12