How do you calculate the probability when you don't know how many trials will be held? You toss a fair coin until you toss two consecutive heads. Find the probability that you have to toss the coins exactly 4 times.
Probability of success on third and fourth trials? I have a pretty basic probability question, but I'm just having difficulties remembering what distribution this is.  A coin is tossed until a head appears two times in a row. Given that we are using a fair coin, what is the probability that we toss the coin exactly 4 times such that the two consecutive heads are the 3rd and 4th trials?  I know that this would be fairly easy to solve by brute force and listing out the different probabilities, but I'm a little confused as to how to use a "shortcut" such as identifying this as a binomial distribution. I also don't know how to account for the probability that we are using 4 tosses.  Any help is appreciated. Thanks!
Did regular Americans speak the way actors in the 30s and 1940s did? I watch a lot of old movies, and I've noticed that American actors of the 1930s and 1940s often spoke in a quasi-generic-posh-British accent.  Katherine Hepburn's accent would be the perfect example. It seems exaggerated, and I imagine it was not common off the stage and screen. What was that? Was it just an accent or was it a dialect? Did real people actually speak that way? I have two separate Armatures that I want to join together. I have no problem combining the meshes, but the problem is the bones/rigs. When you do the Object mode > join, I lose all of my weight paint on one of my armatures. Is there any way I can join two separate armatures and keep all the weight paint. I turn my models into XPS and use XNA Lara to view them, but XNAlara cannot use both armatures at once. Is it really possible to break the speed of light by flicking your wrist with a laser pointer? Quoted headings are rendered properly on preview but not when posted With markdown, you can use some dashes for headings. For example, this: Hello ---- this is some other text  renders as this: Hello this is some other text This is fine and works well. When I want to quote that text is when the problem arises, since this Markdown: &gt; Hello &gt; ---- &gt; this is some other text  When written down shows well in the preview but not when posted:  Hello this is some other text   As an example, see an screenshot of the preview:    and a screenshot of the posted content, where the ---- becomes a &lt;hr&gt;:  Note a similar bug I also reported: . Was PreferenceFragment intentionally excluded from the compatibility package? If Eren Jaeger dies without transfering his titan powers, will both powers transfer to the same child? It's told in the story that if a titan shifter dies without transferring his power, this power will go to an eldian person who just was born. If Eren Jaeger dies without transferring his titan powers, will the attack titan and the founding titan go to different persons?  Note that his is not a duplicate of  as this is not about what happens when a titan shifter dies. But what happens if a titan shifter with 2 powers dies, which is not answered in the answer. How to apply for US passport card when I already have passport book? I have a US passport book, and I would like to apply for a US passport card (to have in addition to my passport book).  If I apply using form DS-82, submitting my current passport book as proof of citizenship, does it get returned to me still valid, or does it get cancelled?  Is it possible to apply for a passport card using form DS-11 and avoid sending in my current valid passport book (submitting a birth certificate instead)?  I would prefer answers with official sources, which I have not been able to find myself on the US State Dept website or on the forms themselves (which are written quite ambiguously). Non abelian Lie group with abelian Lie algebra I'm confused with using single or double brackets. Look at this code:  dir="/home/mazimi/VirtualBox VMs"  if [[ -d ${dir} ]]; then     echo "yep" fi   It works perfectly although the string contains a space. But when I change it to single bracket:  dir="/home/mazimi/VirtualBox VMs"  if [ -d ${dir} ]; then     echo "yep" fi   It says:  ./script.sh: line 5: [: /home/mazimi/VirtualBox: binary operator expected   When I change it to:  dir="/home/mazimi/VirtualBox VMs"  if [ -d "${dir}" ]; then     echo "yep" fi   It works fine. Can someone explain what is happening? When should I assign double quotes around variables like "${var}" to prevent problems caused by spaces? Graduate school admission with a degree in a different field This is a  about DoS and DDoS mitigation.   I found a massive traffic spike on a website that I host today; I am getting thousands of connections a second and I see I'm using all 100Mbps of my available bandwidth.  Nobody can access my site because all the requests time out, and I can't even log into the server because SSH times out too!  This has happened a couple times before, and each time it's lasted a couple hours and gone away on its own.  Occasionally, my website has another distinct but related problem: my server's load average (which is usually around .25) rockets up to 20 or more and nobody can access my site just the same as the other case.  It also goes away after a few hours.  Restarting my server doesn't help; what can I do to make my site accessible again, and what is happening?  Relatedly, I found once that for a day or two, every time I started my service, it got a connection from a particular IP address and then crashed.  As soon as I started it up again, this happened again and it crashed again.  How is that similar, and what can I do about it? I have a list with 15 numbers in, and I need to write some code that produces all 32,768 combinations of those numbers.   I've found  (by Googling) that apparently does what I'm looking for, but I found the code fairly opaque and am wary of using it. Plus I have a feeling there must be a more elegant solution.  The only thing that occurs to me would be to just loop through the decimal integers 1–32768 and convert those to binary, and use the binary representation as a filter to pick out the appropriate numbers.   Does anyone know of a better way? Using map(), maybe? Can I travel to Paris for a day with a single entry visa for Schengen from Switzerland? I am visiting a friend in Switzerland for ten days. I have already got visitor's visa for the same on my Indian passport. Particulars mentioned on my visa are:  1. 'Etats Schengen' , 2. Single entry 3. Dates of visit. &amp; 4. Type of visa : C.  I understand that having already got ‘Etats Schengen' visa, I can travel to all Schengen countries.  I am also planning to visit Paris for a day during my stay in Switzerland. However, I never mentioned this in my visa application. I am planning to take a train from Geneva to Paris and book a hotel in Paris for one night. Can I possibly plan my Paris trip this way as I have Schengen visa, or I am not allowed to travel out of Switzerland as I never mentioned this in my visa application?   Also what does Single entry on my Schengen visa means: does it mean that I can enter and leave Switzerland only once or it means that I can enter and leave the Schengen region only once. How exactly does lighting affect combat? I understand that there are different types of lighting (dim, bright, complete darkness), but I haven't been able to find anywhere in the DMH or PHB that specifically describes how these different types of light sources affect combat.   What impact does complete darkness have on players being able to see the locations of the monsters in the room? What impact does complete darkness have on combat rolls against monsters? Could anyone point me to a book/page that contains some more detailed information on this?   Thanks! Why do Windows 10 foreground apps mysteriously launch as background processes? How can we unlock an iPhone backup file if we don't know the password? Where can I get an Ubuntu Installation CD/DVD/USB? How do I get a file extension in PHP? This is a question you can read everywhere on the web with various answers:  $ext = end(explode('.', $filename)); $ext = substr(strrchr($filename, '.'), 1); $ext = substr($filename, strrpos($filename, '.') + 1); $ext = preg_replace('/^.*\.([^.]+)$/D', '$1', $filename);  $exts = split("[/\\.]", $filename); $n    = count($exts)-1; $ext  = $exts[$n];   etc.  However, there is always "the best way" and it should be on Stack Overflow. Assuming convergence of the following series, find the value of $\sqrt{6+\sqrt{6+\sqrt{6+...}}}$ Assuming convergence of the following series, find the value of $\sqrt{6+\sqrt{6+\sqrt{6+...}}}$  I was advised to proceed with this problem through substitution but that does not seem to help unless I am substituting the wrong parts. If i substitute the $6$, well then i am just stuck with above.   Any ideas on how to proceed. Also, what is the purpose of stating that it is convergent. I don't know why but now, when i go in material preview or rendered (in solid mode it works fine), my object is entirely gray, or invisible idk, because it has the same color of the background. I've been working for days on this project without having this issue, it suddenly showed up. I tried opening other old projects and suddenly they all do the same so i guess it is some blender program setting that applies for all the projects, but idk how it happened cuz i didn't change anything :/, anyone got any tips?