How does a Random number method work? Inclusive or exculsive and rules surrounding it

So I drew a blank as to whether creating a random number was 0 - (specific number) inclusive or exclusive. I created a simple program to test it quickly.

int number;

        Random rand = new Random();
        number = rand.Next(3);
        textBox1.Text = number.ToString();

3 will never occur however zero does. I then add +1

int number;

        Random rand = new Random();
        number = rand.Next(3) + 1;
        textBox1.Text = number.ToString();

Now ofcourse zero doesn't occur, but 3 does.

Why is it allowing 0 but not 3 in the first example? And why in the second does it allow 3? I understand why zero is exempt. Thanks :)