Choose random array element satisfying certain property

Question

Suppose I have a list, called elements, each of which does or does not satisfy some boolean property p. I want to choose one of the elements that

Answer 1

Yes, I believe so.

The first time you encounter a matching element, you definitely pick it. The next time, you pick the new value with a probability of 1/2, so each of the two elements have an equal chance. The following time, you pick the new value with a probability of 1/3, leaving each of the other elements with a probability of 1/2 * 2/3 = 1/3 as well.

I'm trying to find a Wikipedia article about this strategy, but failing so far...

Note that more generally, you're just picking a random sample out of a sequence of unknown length. Your sequence happens to be generated by taking an initial sequence and filtering it, but the algorithm doesn't require that part at all.

I thought I'd got a LINQ operator in MoreLINQ to do this, but I can't find it in the repository... EDIT: Fortunately, it still exists from this answer:

public static T RandomElement(this IEnumerable source,
                                 Random rng)
{
    T current = default(T);
    int count = 0;
    foreach (T element in source)
    {
        count++;
        if (rng.Next(count) == 0)
        {
            current = element;
        }            
    }
    if (count == 0)
    {
        throw new InvalidOperationException("Sequence was empty");
    }
    return current;
}