Generating a random number between multiple ranges

I'd go with something like this, to allow you to do it with as many ranges as you like:

import java.util.ArrayList;
import java.util.List;
import java.util.Random;

class RandomInRanges
{
    private final List<Integer> range = new ArrayList<>();

    RandomInRanges(int min, int max)
    {
        this.addRange(min, max);
    }

    final void addRange(int min, int max)
    {
        for(int i = min; i <= max; i++)
        {
            this.range.add(i);
        }
    }

    int getRandom()
    {
        return this.range.get(new Random().nextInt(this.range.size()));
    }

    public static void main(String[] args)
    {
        RandomInRanges rir = new RandomInRanges(1, 10);
        rir.addRange(50, 60);
        System.out.println(rir.getRandom());
    }
}

First generate an integer between 1 and 20. Then if the value is above 10, map to the second interval.

Random random = new Random();

for (int i=0;i<100;i++) {
    int r = 1 + random.nextInt(60-50+10-1);
    if (r>10) r+=(50-10);
    System.out.println(r);      
}

First, you need to know how many numbers are in each range. (I'm assuming you are choosing integers from a discrete range, not real values from a continuous range.) In your example, there are 10 integers in the first range, and 11 in the second. This means that 10/21 times, you should choose from the first range, and 11/21 times choose from the second. In pseudo-code

x = random(1,21)
if x in 1..10
   return random(1,10)
else
   return random(50,60)