``` wu :: forums (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi) riddles >> hard >> Re: Probability Problem 1 (Message started by: towr on Jun 17th, 2018, 12:14pm) ``` Title: Re: Probability Problem 1 Post by towr on Jun 17th, 2018, 12:14pm [hide]experimentally it's around 36%mathematically, I think it should be 4 times the number of ways to split 8 passengers over 3 non-empty carriages, divided by the number of ways to split 8 passengers over 4 carriages.Which I'd hope would be 4*([5+3-1]!/5!/[3-1]!) / ([8+4-1]!/8!/[4-1]!), but isn't. So I'm making a mistake somewhere[/hide] Title: Re: Probability Problem 1 Post by towr on Jun 17th, 2018, 10:52pm Ah [hide]like railway companies, I had trouble looking at the passengers as individuals.It should be (4*3^8 - 12*2^8 + 12) / 4**8 = 1449/4096 ~= 35.4%[/hide] Title: Re: Probability Problem 1 Post by rmsgrey on Jun 18th, 2018, 4:36pm A quick and dirty program to count all possibilities agrees with towr's second answer.C# code:[hideb]        static void Main(string[] args)        {            int[] pass = {0,0,0,0,0,0,0,0};            int total = 0;            int success = 0;            while (pass[7] < 4)            {                int[] car = { 0, 0, 0, 0 };                for (int i = 0; i < 8; i++)                    car[pass[i] = 1;                if (car[0] + car[1] + car[2] + car[3] == 3)                    success++;                total++;                int j = 0;                pass[j]++;                while (j < 7 && pass[j] == 4)                {                    pass[j] = 0;                    j++;                    pass[j]++;                }            }            Console.WriteLine("{0} successes out of {1} total", success, total);            Console.ReadLine();        }[/hideb]Output: [hide]23184 successes out of 65536 total[/hide] Title: Re: Probability Problem 1 Post by navdeep1771 on Jun 18th, 2018, 8:59pm Your second answer is correct towr. Powered by YaBB 1 Gold - SP 1.4! Forum software copyright © 2000-2004 Yet another Bulletin Board