Choose one of several options with a certain probability.

Question

I have a scenario where I need to show the user a different page for the same URL based on the probability distribution,

so, for example, for 3 pages the distribution may be

page 1 - 30% of all users
page 2 - 50% of all users
page 3 - 20% of all users

When you decide which page to load for a given user, which technique can I use to ensure that the overall distribution matches the above?

I think I need a way to select an object in "random" from the set X {x1, x2 .... xn}, except that instead of all objects being equally likely, the probability of choosing the object in advance is determined.

---

Thanks for putting everyone in, after creating the prototype, this is what I ended up using

private static int RandomIndexWithPercentage(Random random, int[] percentages) {
    if (random == null) {
        throw new ArgumentNullException("random");
    }

    if (percentages == null || percentages.Length == 0) {
        throw new ArgumentException("percentages cannot be null or empty", "percentages");
    }

    if(percentages.Sum() != 100) {
        throw new ArgumentException("percentages should sum upto 100");
    }

    if (percentages.Any(n => n < 0)) {
        throw new ArgumentException("percentages should be non-negative");
    }

    var randomNumber = random.Next(100);
    var sum = 0;
    for (int i = 0; i < percentages.Length; ++i) {
        sum += percentages[i];
        if (sum > randomNumber) {
            return i;
        }
    }

    //This should not be reached, because randomNumber < 100 and sum will hit 100 eventually
    throw new Exception("Unexpected");
} 

Answer 1

0-9. 3, . 8, .

---

, :

private int ChoosePage()
{
    int[] weights = new int[] { 3, 5, 2 };
    int sum = 0;
    int i;
    for (i = 0; i < weights.Length; i++)
        sum += weights[i];
    int selection = (new Random()).Next(sum);
    int count = 0;
    for (i = 0; i < weights.Length - 1; i++)
    {
        count += weights[i];
        if (selection < count)
            return i;
    }
    return weights.Length - 1;
}

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