UPSC NDA Math Model Paper 4

The total number of possible pairs of selected numbers = N = 25 × 25 = 625.
If the numbers match, then both the numbers should be (1, 1), (2, 2), ... and so on.
Let's say that A is the event that both the selected numbers match.
The number of possible cases where the numbers match = n(A) = 25.
And. P(A)=

n(A)

N

=

25

625

=

1

25

.
∴ Probability that the numbers will not match =1−P(A)=

24

25

Hence, the probability of not winning a prize is

24

25

.