06-28-2009, 02:09 PM
In my little series of common errors, I have added a piece on the destruction of Persepolis - or, to be precise, of three of its twelve buildings. In the end, I think I can prove that arson was planned, but it's an argument from probability: it is unlikely that a random fire (by drunken arsonists) destroyed exactly these three, highly significant monuments.
But I got curious; how small is this chance exactly? We're talking about a hypergeometric distribution, but it's more than a quarter of a century ago that I had to solve problems like these. I would say that two problems are involved:
(1)
How many buildings do you want to destroy? There is a 1/12 chance that three of the twelve buildings will be destroyed.
(2)
Then, how great is the chance that a random fire would destroy exactly these three buildings? I would say 3/12 x 2/11 x 1/10.
Summing up, I'd say that there's a chance of 1/12 x (3/12 x 2/11 x 1/10) = 0.037878...% that random arson resulted in the destruction of these three monuments. Am I wrong?
But I got curious; how small is this chance exactly? We're talking about a hypergeometric distribution, but it's more than a quarter of a century ago that I had to solve problems like these. I would say that two problems are involved:
(1)
How many buildings do you want to destroy? There is a 1/12 chance that three of the twelve buildings will be destroyed.
(2)
Then, how great is the chance that a random fire would destroy exactly these three buildings? I would say 3/12 x 2/11 x 1/10.
Summing up, I'd say that there's a chance of 1/12 x (3/12 x 2/11 x 1/10) = 0.037878...% that random arson resulted in the destruction of these three monuments. Am I wrong?