# Greatest integer sums

Algebra Level 2

For two random positive real numbers $$x$$ and $$y$$ chosen uniformly and independently from the interval $$(1,1000)$$, determine the probability that $\lfloor x+y \rfloor = \lfloor x \rfloor + \lfloor y \rfloor.$

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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