Boy born on Tuesday problem

boy-on-tuesday.cs

void Main()
{
	var r = new Random();
	var boy_tue_counts = new Dictionary<InfoSource, Counter>() {
		{ InfoSource.Ask, new Counter() },
		{ InfoSource.Volunteer, new Counter() },
	};
	var boy_counts = new Dictionary<InfoSource, Counter>() {
		{ InfoSource.Ask, new Counter() },
		{ InfoSource.Volunteer, new Counter() },
	};
	const int TOTAL_TRIALS = 500_000_000;
	for (int i = 0; i < TOTAL_TRIALS; i++)
	{
		var kids = new[] {
						RandomChild(r),
						RandomChild(r),
						};
		for (InfoSource src = InfoSource.Ask; src < InfoSource.Max; src++)
		{
			bool boy, boy_on_tuesday, other_is_girl;
			(boy_on_tuesday, other_is_girl) = IsOtherGirl(r, kids, src, k => k.gender == Gender.Boy && k.dayBorn == DayOfWeek.Tuesday);
			if (boy_on_tuesday)
			{
				boy_tue_counts[src].Sample(other_is_girl);
			}
			(boy, other_is_girl) = IsOtherGirl(r, kids, src, k => k.gender == Gender.Boy);
			if (boy)
			{
				boy_counts[src].Sample(other_is_girl);
			}
		}
	}
	var lst = boy_tue_counts.Select(kvp => new { Predicate = "Boy on Tuesday", Mode = kvp.Key, kvp.Value.Hits, kvp.Value.Samples, kvp.Value.Ratio })
	.Concat(
	boy_counts.Select(kvp => new { Predicate = "Boy", Mode = kvp.Key, kvp.Value.Hits, kvp.Value.Samples, kvp.Value.Ratio })
	)
	.ToList()
	.Dump();
}

(bool match, bool other_girl) IsOtherGirl(Random r, Child[] kids, InfoSource mode, Predicate<Child> a_priori)
{
	int match_index;
	if (mode == InfoSource.Volunteer)
	{
		// pick a kid at random and volunteer whether or not they match the predicate
		match_index = r.Next(0, 1);
		var matched = a_priori(kids[match_index]);
		if (!matched) { return (false, false); }
	}
	else
	{
		// asked if any child matches the predicate
		if (a_priori(kids[0])) { match_index = 0; }
		else if (a_priori(kids[1])) { match_index = 1; }
		else { return (false, false); }
	}
	bool other_is_girl = (kids[match_index ^ 1].gender == Gender.Girl);
	return (true, other_is_girl);
}

class Counter
{
	public int Samples;
	public int Hits;
	public double Ratio => (double)Hits / (double)Samples;
	public void Sample(bool isHit)
	{
		Samples++;
		if (isHit) Hits++;
	}
}

public enum InfoSource { Ask, Volunteer, Max }
public enum Gender { Boy, Girl }
public record struct Child(Gender gender, DayOfWeek dayBorn);


static Gender RandomGender(Random r)
{
	if (r.NextDouble() < 0.5) return Gender.Boy;
	else return Gender.Girl;
}
static Child RandomChild(Random r)
{
	var gender = RandomGender(r);
	var dayOfWeek = (DayOfWeek)r.Next(0, 7);
	return new Child(gender, dayOfWeek);
}