Prove-that-if-two-numbers-are-chosen-at-random-then-the-probability-that-their-sum-is-divisible-by-n-is-1-n-

Question Number 785 by rishabh last updated on 12/Mar/15

P r o v e t h a t i f t w o n u m b e r s a r e c h o s e n

a t r a n d o m t h e n t h e p r o b a b i l i t y t h a t

t h e i r s u m i s d i v i s i b l e b y n i s \frac{1}{n} .

Answered by prakash jain last updated on 12/Mar/15

Sum \mod n = k, where 0 ⩽ k ⩽ n - 1 .

All n values for k are equally likely .

hence probability = \frac{1}{n}

Note : It does not matter how many number

you chose at random . It is same as choosing

a sum at random .