Random numbers probability

Question

I am trying to randomly choose from e.g. 4 numbers. I need to compare the probability of these 2 algorithms.

1#

                int a = random.Next(0, 4);

                if (a = 0)
                    statement1
                if (a = 1) 
                    statement2
                if (a = 2)
                    statement3
                if (a = 3) 
                    statement4

2#

                int a = random.Next(0, 1000)

                if (a < 250)
                    statement1
                if (a >= 250 && a < 500) 
                    statement2
                if (a >= 500 && a < 750)
                    statement3
                if (a >= 750) 
                    statement4

Am I right if I think that it is the same ? The probability of statement1 in the first code is 1/4 and in the second code it is 250/1000 so it’s 1/4 too. But someone has told me when I use bigger range of random numbers like in code 2# it’s statistically more accurate. I’ve made project which repeats many times those codes, but I’m not sure it shows me some results.

Answer 1

They are exactly equivalent (except for the fact that the first one won't compile due to using = instead of == in the if-clauses).

To prove this, look at the implementation of Random.Next(int, int). With your values, Random.Next(0, 4) is

(int) (Random.Sample() * 4)

and

Random.Next(0, 1000) is

(int) (Random.Sample() * 1000)

, where Random.Sample() is a private method that returns a random double.

It should now be easy to see that Random.Next(0, 4) will return 0 exactly when Random.Next(0, 1000) will return a number between 0 and 250.