Question

I want to choose randomly* between two alternatives with unequal probability.

For instance, when the user presses a button, 25% of the time it would make sound A and 75% of the time, sound B. I can manually do easy ratios like 1:4 and 2:4 but I’m having trouble with ratios like 3:5.

What is the generic way to think about this?

*I mean unpredictable when looked at one-by-one. I notice any question with
the word random in it gets a Mensa of
pedants.

Answer 1

For 3:5 you can add them together to get 8, and pick a random integer less than 8. If it’s 0, 1, or 2 (three chances) you choose A, and if it’s 3, 4, 5, 6, or 7 (five chances) you choose B. Code-wise you’d just check whether your random number is less than 3.

For something like 3:5:4, you’d pick a random number less than 12 (3+5+4) and if it’s less than 3 you choose A, otherwise if it’s less than 8 (3+5) you choose B, otherwise you choose C.

This can generalize to any number of alternatives, but it’s inefficient with lots of alternatives since you have to check the random number against each threshold, which is O(n). This SO question seems to provide some more efficient (but more complex) algorithms for weighted random selection with larger numbers of alternatives.