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Topic: Re: Probability Problem 1 (Read 661 times) |
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towr
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Re: Probability Problem 1
« on: Jun 17th, 2018, 12:14pm » |
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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
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towr
wu::riddles Moderator
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Re: Probability Problem 1
« Reply #1 on: Jun 17th, 2018, 10:52pm » |
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Ah 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%
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rmsgrey
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Re: Probability Problem 1
« Reply #2 on: Jun 18th, 2018, 4:36pm » |
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A quick and dirty program to count all possibilities agrees with towr's second answer.
C# code:
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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();
}
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Output: 23184 successes out of 65536 total
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navdeep1771
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Re: Probability Problem 1
« Reply #3 on: Jun 18th, 2018, 8:59pm » |
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Your second answer is correct towr.
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