how many missiles would be needed to ensure a better than evens chance of more than two missiles evading the defenses?
I got: $1 - 0.995^n - \left[(0.005^n) \times (0.995^{n-1}) \times n\right] - \left[(0.005^2) \times (0.995^{n-2})\times \frac{n(n-1)}{2}\right] = \frac{1}{2}$
when compute numerically I got 263 from wolfram whilst the book says 535
You wrote $(.005^n)$. You should have written $(.005^1)$. If you try solving it again, you should get the right answer. Based on the rest of your work, it seems like you know what you're doing, and this was just a typo.