# An interesting (and famous) probability

Let $${P}_{N}$$ be the probability that two randomly selected integers on the interval $$\left[ 1,N \right]$$ are coprime. Evaluate $\lim_{N \to \infty}{P}_{N}$

Notes:

Two integers $$a$$ and $$b$$ are coprime if and only if $$gcd\left( a,b \right) =1$$

Round your answer to $$3$$ decimal places, and express as a decimal instead of a percent (Not $$92.4$$%, instead enter $$0.924$$).

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