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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?

 Dec 5, 2021
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2 numbers out of 100 can be summed up in:

 

100 C 2 ==4,950 ways

 

Out of 4,950 ways, there are 1,225 ways of adding up 2 numbers whose sum is divisible by 4

 

So, the probability is: 1,225 / 4,950 ==25 / 99

 Dec 6, 2021

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