Ball and drawer principle (aka modified pigeonhole)

Consider a drawer full of balls of two colour - Black and White. Alice randomly selects one ball and takes it out. Then the same way she randomly selects another ball.

Given that the number $n$ of black balls satisfies the condition that the probability that the two balls Alice chose are White is $\frac{1}{2}$ , and such that $n$ is a $7$ -digit number, find $n \pmod {1000}$ .