# I'm not drawing it for you!

**Discrete Mathematics**Level 5

Two circles, A and B, with radii of length equal to 1 are built on the \(xy\) plane. The center of A is chosen randomly and uniformly in the line segment that starts at \((0,0)\) and ends at \((2,0)\). The center of B is chosen randomly, uniformly, and independently of the first choice, in the line segment that starts at \((0,1)\) and ends at \((2,1)\). Let \(P\) be the probability that the circles A and B intersect. Find: \[ \left\lfloor {10^4 P + 0.5} \right\rfloor \] Note: \(\left\lfloor x \right\rfloor \) represents the integral part of \(x\), that is, the greatest integer lower or equal than \(x\). Example: \(\left\lfloor {1.3} \right\rfloor = 1\), \(\left\lfloor { - 1.3} \right\rfloor = - 2\).