algorithm - generate random numbers within a range with different probabilities

Question

How can i generate a random number between A = 1 and B = 10 where each number has a different probability?

Example: number / probability

1 - 20%

2 - 20%

3 - 10%

4 - 5%

5 - 5%

...and so on.

I'm aware of some hard-coded workarounds which unfortunately are of no use with larger ranges, for example A = 1000 and B = 100000.

Assume we have a

    Rand()

method which returns a random number R, 0 < R < 1, can anyone post a code sample with a proper way of doing this ? prefferable in c# / java / actionscript.

Answer 1

Build an array of 100 integers and populate it with 20 1's, 20 2's, 10 3's, 5 4's, 5 5's, etc. Then just randomly pick an item from the array.

int[] numbers = new int[100];
// populate the first 20 with the value '1'
for (int i = 0; i < 20; ++i)
{
    numbers[i] = 1;
}
// populate the rest of the array as desired.

// To get an item:
// Since your Rand() function returns 0 < R < 1
int ix = (int)(Rand() * 100);
int num = numbers[ix];

This works well if the number of items is reasonably small and your precision isn't too strict. That is, if you wanted 4.375% 7's, then you'd need a much larger array.