Natural selection!

Probability Level 3

A natural number xx is selected from the set of the first 100100 positive integers. Find the probability that it satisfies the inequality: x+100x>50 x + \dfrac{100}{x} > 50 If the probability is of the form ab \dfrac{a}{b} , where a and b are coprime integers, find the value of a+b a + b .

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