#984 – The Birthday Problem

To celebrate today’s Thanksgiving holiday in the United States, the post today is just a fun little code fragment for exploring the birthday problem.  The idea of the birthday problem is to look at the probability of having at least one shared birthday in a group of n people.

Instead of calculating the actual probability of a collision, the code below empirically creates a group of people, assigns them birthdays, and then looks for shared birthdays.  It does this 100,000 times and then reports what percentage of time there actually was a match.

        static void Main(string[] args)
            while (true)
                Console.Write("Enter # people: ");
                int numPeople = int.Parse(Console.ReadLine());

                const double NumTrials = 100000.0;

                int numBirthdayMatches = 0;
                double numUniqueBirthdaySum = 0;

                List<int> personBirthdays;
                Random rnd = new Random();

                for (int trialNum = 1; trialNum <= NumTrials; trialNum++)
                    // Generate birthdays
                    personBirthdays = new List<int>(numPeople);
                    for (int personNum = 1; personNum <= numPeople; personNum++)
                        personBirthdays.Add(rnd.Next(1, 366));

                    if (personBirthdays.Count != personBirthdays.Distinct().Count())

                    numUniqueBirthdaySum += personBirthdays.Distinct().Count();

                double percentMatched =
                    numBirthdayMatches / NumTrials * 100.0;
                double numUniquePerTrial = numUniqueBirthdaySum / NumTrials;
                Console.WriteLine(string.Format("For {0} people, there was at least one matching birthday {1}% of the time.  Avg # unique birthdays={2}",




About Sean
Software developer in the Twin Cities area, passionate about .NET technologies. Equally passionate about my own personal projects related to family history and preservation of family stories and photos.

2 Responses to #984 – The Birthday Problem

  1. Pingback: Dew Drop – December 2, 2013 (#1674) | Morning Dew

  2. Brian says:

    Very similar to the Monty Hall problem (http://en.wikipedia.org/wiki/Monty_Hall_problem). Another fun one that’s easy to implement and prove via code.

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