Logic similar to this should work. You want to save the user input to a String variable, and then compare it to an n sized array.
for(int i=0; i<arrayName.length();i++)
{
if(userinputString.equalsIgnorCase(arrayName[i])
{
System.out.println("HUrray!");
}//end if
}//end for
Ok so you are somehow producing a random number, and then need to compare the input to the String in the capital Array for that random number/
Im assuming the arrays are ordered such that capitals[10] gives you the capital for states[10].
If so, just save the index to a variable.
int ranNum=RandomNumFunction();
Then just see if
if(capitals[ranNum].equalsIgnoreCase(userInput))
//do something