Kedas Posted December 10, 2007 Share Posted December 10, 2007 If you have an ordered list of numbers and you randomly change them what is the chance that at least one number will stay on its previous position? Or more practically if you give everyone a number and you let them blindly pick a number. What is the chance that at least one persons picks his/her own number again. Link to comment Share on other sites More sharing options...
Tartaglia Posted December 12, 2007 Share Posted December 12, 2007 1-(1/n) Link to comment Share on other sites More sharing options...
Kedas Posted December 13, 2007 Author Share Posted December 13, 2007 It looks right for n=2 and n=3 but n=1 should be 1. and if n is very large than the change that at least one stays at its current position is very high. So if I have a cube of water and give it a good (random) shake. Then I can say it is very likely that at least one molecule arrived on it's previous position. That sounds a bit weird? Link to comment Share on other sites More sharing options...
Tartaglia Posted December 13, 2007 Share Posted December 13, 2007 The working is Prob(>= 1) = 1 -P(0) = 1 - (n-1!/n!) = 1 - (1/n) for n> 1 In the case of n = 1, P(>= 1) = 1 - 0/1 = 1. The failure comes from definition of 0! = 1 Link to comment Share on other sites More sharing options...
Kedas Posted December 13, 2007 Author Share Posted December 13, 2007 Thanks for the explanation 1-((n-1)!/n!) looks more right because it doesn't look too simple Link to comment Share on other sites More sharing options...
uncool Posted December 14, 2007 Share Posted December 14, 2007 Not quite - P(0) is not (n-1)!/n!. For example, P(0) for 4 is 3/8, not 1/4. The actual answer is: 1/1! - 1/2! + ... + (-1)^(n - 1)/n! (iirc). See http://en.wikipedia.org/wiki/Derangement =Uncool- Link to comment Share on other sites More sharing options...
Tartaglia Posted December 15, 2007 Share Posted December 15, 2007 Quite right uncool - I do apologise. I didn't consider that there are two types of numbers after one has been chosen.Those whose positions are taken and those whose positions aren't Link to comment Share on other sites More sharing options...
Kedas Posted December 17, 2007 Author Share Posted December 17, 2007 Thanks uncool. My weird 'feeling' example feels much more right now Link to comment Share on other sites More sharing options...
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