A friend of mine (an I.T. guy) gave me this tricky probability problem, that I couldn't solve.  $n$ persons go to a cinema that has $n$ seats, and everyone of them has an assigned position written on the ticket.  The first person $p_1$ commits an error and chooses the wrong seat.  Then $p_2,\ldots,p_n$ arrive (in order) and they choose their seat according to the following rule:  "If the assigned seat is free, go there. Otherwise, choose a random seat among the free ones."  What is the probability for the last person $p_n$ to sit in his assigned seat?
This is a neat little problem that I was discussing today with my lab group out at lunch. Not particularly difficult but interesting implications nonetheless  Imagine there are a 100 people in line to board a plane that seats 100. The first person in line realizes he lost his boarding pass so when he boards he decides to take a random seat instead. Every person that boards the plane after him will either take their "proper" seat, or if that seat is taken, a random seat instead.  Question: What is the probability that the last person that boards will end up in his/her proper seat.  Moreover, and this is the part I'm still pondering about. Can you think of a physical system that would follow this combinatorial statistics? Maybe a spin wave function in a crystal etc...
Ignoring somebody screws up the avatar list When I ignore a user, the avatar list looks weird.    The blank line beneath the row with the avatar of the ignoree is quite annoying.    I use Google Chrome on OS X.  There was a  tagged  but it still looks weird. Do votes get canceled if voting privilege is lost? If I'm below 15 reputation, I can't alter the public score of an answer/question.  Suppose I gain the privilege by getting the required rep and vote some posts up. Then, for any reason, I fall below 15 and lose the ability to vote. What about the votes I already did cast?  Do post scores get altered by ignoring my vote, or will they stay the same? In other words, is losing a privilege retroactive?  If yes, what about when I gain my privilege back? Are my votes automatically restored, or do I have to cast them again from scratch?  I made the easiest example, but this applies to any higher privilege What would you call a word that doesn't exist in or translate well into another language? Within 300 km of Tokyo: Where for flora, landscape, nature? I plan to visit Japan for 10 days and apportion 5 days to Tokyo. For the remainder, I want to escape the megalopolis and enjoy picturesque backwoods or countryside. Please recommend? Criteria:   No dangerous animals or untamed boondocks. No  or snakes. I won't drive, and must rely on public transport and walking less than 5 km in total.  No shrines, temples or any religious edifice. OPTIONAL: I fancy  , the more  the better.   This instantiates, doesn't duplicate, . With spells like Moonbeam or Flaming Sphere, how should we treat the movement of their areas-of-effect when it comes to passing them behind a thick pillar or around a blind corner?  Should we treat any movement of them as if they are being 're-cast' (and so requiring a clear unobstructed view)? Or could a mage presumably will them somewhere out-of-sight? The Raspberry Pi B+ models have a protection circuit between the USB connector and the 5V net on the board.  They recommend putting a similar protection circuity on a Pi HAT before 'backpowering' the pi through its GPIO header along with a polyfuse.  I understand why this is the recommendation, but I'd like to understand more about how this circuit works.  I did some searching before posting this question and found information on using a MOSFET as a low voltage drop diode, but they all had the gate wired directly to ground without the pair of PNP's and the resistors.  What are they doing for this circuit?  Also, is this primarily using the body diode?  In which case, what's the relevant info on the datasheet that qualifies DMG2305UX for this application?  In the other circuits I found, it appeared low Rdson and Vgsth compatible with the circuit seemed like the relevant characteristics. How does ${!#} work in bash to get the last command-line argument? From the Advanced Bash-Scripting Guide, to get the last command-line argument:     Or: lastarg=${!#}    This is an   indirect reference to the $# variable.    Note that lastarg=${!$#} doesn't work. I have downloaded and extracted the packet tracer file, then I used this command as root  chmod +x install   then I ran (as root)  ./install    Then I used this command   ./set_ptenv.sh   but whenever I run this command   packettracer    it just doesn't start What is this weird colon-member (" : ") syntax in the constructor? How to provide a file download from a JSF backing bean? I am trying to install Ubuntu 12.10 for quite some time, and passing hurdles one by one. Now I am in a situation as follows.  I have got a PC and 10 GB HDD which will be totally dedicated to Ubuntu so no option of Wubi and dual boot.  I was trying to install from DVD, but it is getting stuck at "Out of frequency" error. So I had to adapt for USB boot option. But my PC is USB non bootable, so workaround is "Plop Boot Manager". So I am doing the installation procedure as follows:   starting  from a CD drive which is having plop installed. opting for for USB boot in plop options. booting begins from USB. monitor eventually gives "out of frequency" error press Shift+Alt+F1 to get the terminal. open the grub with sudo nano /etc/default/grub. do necessary changes. sudo update-grub.   Now here I am getting error as follows:   /usr/sbin/grub-probe:error:failed to get canonical path of /cow.     My system is   P4 3.06 GHz, 1 GB ram , 10 GB HDD without an OS, monitor CRT lg StudioWorks (7 years old). Mobo Mercury P4 266a NDMx (865 equivalent). The whole system is perfectly in working condition under XP, but it is USB non bootable, and all other devices working perfectly.  What should I do next? Freeze vertical columns in horizonal scrolling visual force page (like excel freeze pane) let's say have 20 columns total.   I want to fix till 5 columns. (means only important ID, etc will be fixed while doing horizonal scrolling)  How can I achieve it in Visual Force Datatable ? Word for "someone who talks too much" 12.04 GPU lockup I was able to install Ubuntu 12.04 using the alternative version of the image, (64 bit) but when I start the system it tells me the GPU  locked up, and instead presents a text only screen.  I understand that this site is not for bug reports, but at the same time, I know that there are some versions of the installer than have to be compatible with my graphics card (Nvidia GTS 360M).  I assumed that the mere fact that the alternative installer ran was an indication that I could get some sort of graphical interface running after the install.  Is there some way of getting some type of graphical interface running on my machine? Even better would be is there a way to get the rest of the system running as normal (i.e. GPU up and running)?  If an internet connection is required to download driver support or something similar, directions for how to configure a wireless connection with WPA2-Personal protection from the text-only interface (bash).  Any help would be appreciated.  Note: I was able to find  which tells me that the card is supported.  Note 2: In the install software stage of the install, I was unable to install anything (no internet connection)  Update: The exact error message is [8.591394] [drm] 0000:01:00.0: GPU Lockup - switching to software fbcon  Update 2: If I try to install with the regular version of Ubuntu, the screen goes staticy. This also happens if I install with Wubi (distasteful I know) and then try to use Ubuntu.  Update 3: I've tried xforcevesa, nomodeset and xforcevesa nomodeset as my wubi boot options.  Update 4: Thanks to jokerdino, I can now connect to the internet, so internet tools would now be a possibility. Cannot see files in my external HDD Finding center and radius of circumscribed triangle If apostrophe + s is the acceptable way of denoting a genitive in English, is it possible that possessive pronouns, such as hers, ours and yours, started life as possessive adjectives with apostrophe + s?  E.g. her's, our's, your's, their's? Perhaps, even his' ? Its and my obviously stick out from this tempting pattern.  Is there any evidence that this might be the case, or is the 's completely unrelated? Can you make an opportunity attack against a moving object? How can I add an application to the GNOME window manager? The GNOME on-board documentation covers only the things anyone can easily guess. I have an application for that I can only start from the command line. Not that I mind using a terminal but ...  Anyway, how do I add the command (and preferably a nice logo) to GNOME WM? I've got a generic dictionary Dictionary&lt;string, T&gt; that I would like to essentially make a Clone() of ..any suggestions.