Suppose we want to pick two numbers from {1,2,⋯,100} randomly. What is the probability that the sum of the two picked numbers is divisible by 4?

100 C 2 ==4,950 ways of picking 2 numbers.

Of those 4,950 combinations, there are:

25 x 49 == 1225 ways of getting multiples of 4.

Therefore, the probability is: 1225 / 4950 ==49 / 198