Let's say that you have an arbitrarily large sized two-dimensional array with an even amount of items in it. Let's also assume for clarity that you can only choose between two things to put as a given item in the array. How would you go about putting a random choice at a given index in the array but once the array is filled you have an even split among the two choices?

If there are any answers with code, Java is preferred but other languages are fine as well.