I have been thinking about one problem, which is not understandable to me. Consider the following: I have a deck of cards (52 cards). I pick card after card (no replacement), but I stop when the current card belongs to the same family (Aces, Kings, etc.) as the card picked before. The number of observations is an event, so we can say in our sample space there are 50 events (2-52), BUT we should add another, which is that nothing happens at all. This last part gives me a huge headache and I don't know how to consider even start thinking about a problem and create a formula for this problem, such as find probability for the formula for an event. I would really really appreciate it if someone could help me understand this problem. Thank you. edit: the current card must match the card picked before, not any card picked before.
What is the probability that a shuffled standard deck of 52 cards has no two cards of the same rank together ?  I am unable to get a handle on this problem, and wonder whether there is an analytical solution ?
Are "white" and "black" ever capitalized when referring to people? In  Deathly Hallows, when Harry, Ron, and Hermione are at No. 12, Grimmauld Place, Harry summons Kreacher from the kitchens at Hogwarts where the elf has been working on Harry’s orders given a year previously.  When the trio’s heist in the Ministry of Magic ends with Hermione inadvertently bringing Yaxley inside the perimeter of the Fidelius charm that protects Grimmauld Place, the trio leg it and dare not return there for fear that it’s now crawling with Death Eaters.  Before they leave for the Ministry in the morning, Kreacher is talking about making a stew or pot roast or something for dinner. After the trio go on the run and camp out in the tent, Harry thinks of poor Kreacher preparing a dinner they’ll never return to eat, but they dare not summon him lest a Death Eater tag along (like how Dobby ‘tagged along’ with Kreacher when Harry called him to have him follow Draco in Half-Blood Prince).  The next time we see Kreacher is during the Battle of Hogwarts where he leads the house-elves from the kitchen with battle-cries of “For Master! For Harry Potter!” (or something like that), so he’s clearly lost none of his new-found loyalty to Harry.  Harry is still Kreacher’s master throughout the book, and since he does not communicate at all with Kreacher after their escape from the doorstep, he cannot have ordered Kreacher to return to Hogwarts to work there again.  We know that house-elves can go against their masters’ wishes, but this usually entails them punishing themselves rather brutally, and Kreacher does not seem to have been constantly injuring himself for the better part of a year at Hogwarts.  So when and how does Kreacher leave his master’s house without orders and return to Hogwarts? I'm a Canadian citizen with a Canadian passport. I booked a flight with American Airlines to Mexico City From Toronto Pearson and it says that "Passenger details are needed to check in".  Flight 1: YYZ -> DFW -> MEX Flight 2: MEX -> DFW -> YYZ     They already took my name, gender and such. It is now asking for my passport number and expiry date. That all seems reasonable. However, when I enter that I am a Canadian resident it asks for:  1) Street or hotel in US 2) City in US 3) State in US    My trip to DFW is only for a connecting flight. The fields are required so I can't submit my passport information without filling this in.    Is there something I'm missing? Take most recent (or concatenate) edit comments when editing during grace period Recently, I edited  to update a link to a better resource. I clicked "Save" without entering a description of the edit (edit #1).  Then I realised that the question was asked by a new user who may not be able to easily identify the change that was made. So I edited it again, this time only to add a detailed edit description (edit #2).  Since edit #2 was made during the grace period (within 5 minutes of edit #1), the system has merged them into a single edit, but only the edit comment from edit #1 was recorded in the revision history, whereas edit #2's comment was simply discarded/ignored.  I'd suggest that either the most recent (non-default) edit comment is taken or that the comments are concatenated to provide a more useful edit history Is every metric space a subspace of some connected metric space? How can I contribute to Ubuntu? I would like to know what kinds of contributions someone can make to Ubuntu. Such as Programmer, User, Proofreader, etc. Prove that $\sum_{n=1}^{\infty}\exp\left(-n^{\varepsilon}\right)$ converges. String manipulation with & or + in VB.NET What partitioning scheme do you recommend for a desktop? I've always created three or four primary partitions -- root, swap, home, and sometimes a separate boot partition. Ubuntu's default install offers LVMs. I've never had to add additional drives or space, so it never seemed like a big deal. Whenever I do a fresh install, though, I always think there might be a better way. How can I improve Ubuntu overall system performance? What are your tips for improving overall system performance on ubuntu? Inspired by this  I realized that some default settings may be rather conservative on Ubuntu and that it's possible to tweak it with little or no risk if you wish to make it faster.  This is not meant to be application specific (e.g. make firefox load pages faster), but system wide.  Preferably 1 tip per answer, with enough detail for people to implement it.  A couple of mine would be:   Install  (via Software Center or sudo apt-get install preload); Change  value - "which controls the degree to which the kernel prefers to swap when it tries to free memory";   What are yours?  PS: Since this is not intended to have a unique answer but rather, several useful tips, I'm making this community wiki out-of-the-box. How to NOT show keyboard layout chooser popup when changing language in GNOME 3 Control Android with broken screen from PC Since Ubuntu 11.10 use a new kernel, it's very difficult to have a decent support for virtualization.   VirtualBox doesn't support guest additions for ubuntu 11.10, so I can't copy to and from my ubuntu desktop and windows, which I absolutely require, plus FreeBSD seems not to be able to use DHCP without guest additions.  Virt-manager instead gives an error on launch:  Unable to open a connection to the libvirt management daemon.  Libvirt URI is: qemu:///system  Verify that:  - The 'libvirt-bin' package is installed  - The 'libvirtd' daemon has been started  - You are member of the 'libvirtd' group   unable to connect to '/var/run/libvirt/libvirt-sock', libvirtd may need to be started: Permission denied  Traceback (most recent call last):   File "/usr/share/virt-manager/virtManager/connection.py", line 1146, in _open_thread     self.vmm = self._try_open()   File "/usr/share/virt-manager/virtManager/connection.py", line 1130, in _try_open     flags)   File "/usr/lib/python2.7/dist-packages/libvirt.py", line 102, in openAuth     if ret is None:raise libvirtError('virConnectOpenAuth() failed') libvirtError: unable to connect to '/var/run/libvirt/libvirt-sock', libvirtd may need to be started: Permission denied   The problem is solved by running virt-manager as root, but I don't like that. How do I change permissions to run Virt-Manager as user?  Is there a way to install guest additions on Ubuntu 11.10? Referring to correctly-styled algpseudocode procedure name in document Given an algorithm written in algpseudocode:  \documentclass{article} \usepackage{algorithm} \usepackage{algpseudocode} \begin{document} \begin{algorithm}   \caption{Part 1}   \begin{algorithmic}[1]     \Procedure {FooProc}{$G$}       \State ...     \EndProcedure   \end{algorithmic} \end{algorithm} \end{document}   How can I now refer to FooProc in my document (outside of the algorithm environment) such that it has the same typeset as in inside the algorithm environment? Read MIME data using PHP To show that $2$ | $x^{2n} - x^n$, $n \in \mathbb{Z^+}$ is the following adequate? Show that $2$ | $x^{2n} - x^n$, $n \in \mathbb{Z^+}$   Let $x^n = a$ then $\frac{a}{2}$ $\implies a = 2q + r$ such that $r = 0 \vee r = 1$.   So $x^{2n} = (x^n)^2 = a^2 = (2q + r)^2$, which means that $2|[x^{2n} - x^n ]= 2| [(2q + r)^2 - (2q + r)]$. If $r = 1$ we get $(4q^2 + 4q + 1) - 2q - 1 = 4q^2 + 2q = 2(2q^2 +1)$. Thus $2$|$x^{2n} - x^n$, $n \in \mathbb{Z^+}$. Is this reasoning correct? Is it adequate? In Ex Machina, can this character survive? Smooth option sometimes produces incorrect arrow tips in PGFplots Beamer, page/frame numbers, buttons and Appendix slides I want to remove the URL that gets printed on the bottom of the page.   like:  yomari.com/.../main.php?sen_n   How can it be omitted or prevent from getting printed?  To be more specific, is there any way I can prevent the page URL, date and the page title being printed along, while printing the web page?