Using the properties of the power law for extreme value theory, the probability follows the relationship: P(v > x) = K * x^(-α)

Given that for x = 100, P(v > 100) = 0.1, and α = 2, we can find K: 0.1 = K * 100^(-2) K = 0.1 * 100^2 = 0.1 * 10000 = 1000

Now, we can find the probability for x = 200: P(v > 200) = K * 200^(-2) P(v > 200) = 1000 / 40000 = 1/40 = 0.025.