How choose random number within range, but weighted toward one part of that range? (in Java)

Question

I want to choose random numbers within a range of numbers, but with weighting towards part of that range. For example:

1. Choose random number between 1-10
2. Weight it so that 1-5 is maybe 20% more likely than 6-10

Is this possible? How would I do this?

Answer 1

It depends on how you want your probability distribution to look like.

For example:

Pick a random number between 1-10
If it is <= 6
    Return a random number between 1-5
Else
    Return a random number between 6-10
EndIf

Picks a number in 1-5 60% of the time and a number in 6-10 40% of the time.

Answer 2

To generate a bell curve of probabilities, roll and sum multiple dice. Then subtract the average. Re-roll if the result is negative. The more dice rolled, the more weighting.

Here's one way, wholly untested.

float sum;
do {
   sum = rollThreeDice(); // returns 3 to 18, with an average is 10.5
   sum -= 10.5;           // Now the range is 0 to 7.5, with the lower end being more likely.
   } while(sum < 0);
return sum;

Of course you can roll dice with any number of sides in order to produce the desired range. You control the frequency curve by choosing the number of dice.