What is the probability the maximum sample value comes from one of two random distributions?

Question

Let $X_1$ and $X_2$ be randomly distributed variables with means $\mu_1$ and $\mu_2$ and standard deviations $\sigma_1$ and $\sigma_2$. Samples of size of $n_1$ and $n_2$ are drawn from each distribution. What is the probability that the maximum value drawn will come from the distribution for $X_1$?