I sample independently $n$ data points following normal distribution with $\mu = 0$ and $\sigma = 1$. Then I divide the sample into two groups $G_1$ and $G_2$ of sizes $g_1$ and $g_2$ respectively ($g_1 + g_2 = n$). What is the probability that all the values in the group $G_2$ will be greater than any of the value in $G_1$?
The interest arises from the fact that if I analyze a huge data set consisting of a tremendous amount of variables what is the chance that some of the variables (if I assume their independence) will be potentially significant.
Thanks for nice answers and comments. I think, I stated my question wrongly. I know exactly how I will divide my sample into two groups $G_1$ and $G_2$. So, the division is not random.
Regarding the comment about the connection between the first and the second paragraph: If I have a large data set, I would like to estimate how many variables could behave "significant" at random (for example, if I apply univariate rank test for every variable). I sample every variable from the aforementioned normal distribution. When sampling is finished, I divide the sample always in the same way to $G_1$ and $G_2$. At the end I probably get a table corresponding to $p$ sampling procedures of $n$ values that I divide into $2$ groups. One thing, I'm interested in small $n$ and almost equal $g_1$ and $g_2$.