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A simple probability question!
Hi,
I am having difficulty with the following problem: You can have a state of 256 different elements (0-255). An element between 0-255 appears only once in a state of 256 elements. I understand that there are N! possible states. Now I want to calculate the probability of a state that has some k elements (not necessarily consecutive) common with a state that I have picked. Any suggestions on how to approach this problem? I apologize for the ignorance if it is too simple. Thank you! |
#2
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Re: A simple probability question!
Could you be clearer in your description of your problem? |
#3
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Re: A simple probability question!
[ QUOTE ]
Could you be clearer in your description of your problem? [/ QUOTE ] It seems he is asking: Given 2 permutations of 256 distinct elements, what are the odds that they will agree on (exactly?) k elements? ( the N! seems to imply he is talking about permutations, as does the "only appears once" ) |
#4
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Re: A simple probability question!
Hi,
My apologizes for the confusion. It is infact permutation of 256 elements (N! is nothing but 256! ways of arranging 256 unique elements = permutation). Let me elaborate the question by first defining k-state: A k-state is a partially defined state that includes k elements (not necessarily consecutive). Now let 'A' be a k-state and let 'E' be the event that the current chosen state (one picked from 256! states) has the same k elements as 'A'. So what is P[E]? If you need more information please let me know. Thanks for your effort in solving this for me. Sincerely. |
#5
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Re: A simple probability question!
To me, your question still makes no sense.
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#6
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Re: A simple probability question!
[ QUOTE ]
Hi, My apologizes for the confusion. It is infact permutation of 256 elements (N! is nothing but 256! ways of arranging 256 unique elements = permutation). Let me elaborate the question by first defining k-state: A k-state is a partially defined state that includes k elements (not necessarily consecutive). Now let 'A' be a k-state and let 'E' be the event that the current chosen state (one picked from 256! states) has the same k elements as 'A'. So what is P[E]? If you need more information please let me know. Thanks for your effort in solving this for me. Sincerely. [/ QUOTE ] If you mean that E must agree with A in k specific places (and it can agree in other places too), then the number of possibilities for A is (256-k)!, and P(E) = (256-k)!/256! = 1/[ k!*C(256,k) ] = 1/P(256,k). Let me know if you wanted something different. |
#7
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Re: A simple probability question!
Hi BruceZ,
Thank you so much. Your answer is very convincing. Please note that A is only partially defined i.e only k elements are defined and not the rest. So E can agree with A on only k specific elements and not more. However that does not change the final answer. Sincerely, |
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