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In our math book it is written that if you want to go to a random point in a $1D$ place and you randomly go right and left and also you have unlimited time finally you arrive at that point. Also in a $2D$ place you finally arrive there. But in a $3D$ place the chance to arrive there is 24%. It is really amazing but our book don't bring any proofs for it. How can we know this?

Qaswed
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Taha Akbari
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  • with the probability of $\frac{24}{100}$ you arrive that point in unlimited time. – Taha Akbari Jun 21 '16 at 11:02
  • @NP-hard.Our book is written by persion language you cannot understand it. – Taha Akbari Jun 21 '16 at 11:09
  • This was question #536 on this site -- I think this is the first time I encountered a three-digit question number :-) Note that while the duplicated question only explicitly adresses the low-dimensional cases, some comments and links under the answers also address the high-dimensional case. – joriki Jun 21 '16 at 11:18
  • @joriki.I want to know why we have the probability of $24$% on $3D$ walk. – Taha Akbari Jun 21 '16 at 11:19
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    It doesn't. The MathWorld page linked to in the other thread gives that probability as approximately $34%$. If you're specifically looking for a proof of that probability, I'd suggest to edit the question to make that clear and to link to the existing thread on the low-dimensional cases -- shall I do that or do you want to do it? – joriki Jun 21 '16 at 11:24
  • Are you sure it is $34$% but I looked again in my book and it was $24$%. – Taha Akbari Jun 21 '16 at 11:26
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    Well, nowadays we have the Internet to check books. A brief search confirms that the typo is in your book and not in MathWorld. – joriki Jun 21 '16 at 11:29
  • Where have you looked I cannot find it. – Taha Akbari Jun 21 '16 at 11:32
  • Note that you automatically get notified when I write here because this is your question, but I don't get automatically notified when you write, so if you want to ask me something you need to ping me (using the @username construct). I'm off to lunch now but will post some links later. – joriki Jun 21 '16 at 12:30
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    In addition to the MathWorld article, there's Wikipedia, an OEIS sequence, an MO question and, since you seem to like those, a book. – joriki Jun 21 '16 at 16:37
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    Note that the MathWorld article gives several references for the result. If you still want to ask how to prove it, I can reopen the question if you edit it to reflect the existing question on the low-dimensional cases; or let me know if you want me to do it. – joriki Jun 21 '16 at 16:39
  • @joriki. no it isn't needed. – Taha Akbari Jun 21 '16 at 19:32

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