I understand that each toss has a 50% chance if it is a fair coin, but I have hard time grasping the law of great numbers and I would like to know how likely it is that I get 20 heads in a row in such a large number of tosses.  Btw, is there really any difference if the coin IS NOT fair?  Lets say that I only have a 47.5% chance of winning, does that increase the probability of getting 20 heads in a row?  Regards,
Each event has two possible outcomes: a and b.  Each event is independent.  Outcome a has $X\%$ chance of happening.  If we run $Y$ number of such events, what are the chances of getting $K$ outcomes a in a row, at least once?  To put it in practical terms imagine a series of coin tosses. Each coin toss has two possible outcomes: a = heads and b = tails. Outcome a = heads has a chance of $50\%$. If we run $Y = 100$ number of coin tosses, what are the chances of getting $K = 10$ outcomes a=heads in a row, at least once?   I'm using the practical example only so I can express the idea more clearly. I'm interested in finding out the general formulas and computations so that I can run the calculations for any $X$, $Y$, or $K$.  I would also be very interested in knowing how the probabilities would change if the events would not be independent. What if the more outcomes a we have in a row the bigger the chance of getting an outcome a in the next event? What if it's the other way around, and the more outcomes a in a row we have the lower the chance of getting another a?
Arriving at a different port of entry in the same state in USA? I am a girl in my early twenties traveling to USA from India and in my visa application I have provided the contact address for a relative in San Francisco, and their invitation letter. I would like to visit LA first. Will I face problems during immigration if I land in LA (with an immediate on wards ticket to SF)? I dont plan to get on the flight from LA to SFO.  Initially I was planning to fly to SFO from India and then fly to LA immediately after completing immigration at SFO airport. Do multi-use keys get discarded when finished with? As with many resident evil games, you sometimes needs to collect certain keys to open certain doors, and resident evil 7 has plenty of these around.  Some keys are clearly single use, and get left in the lock in which you use them. However, there are a number of keys that can be used on multiple doors. For example, the Scorpion Key.  I am concerned that I might end up carrying these around needlessly and using up valuable inventory space, so...  Do these multi-use keys get discarded when you use them on all the doors they apply to? Or do you get a warning saying the key is no longer needed? (like previous games are known to do) How to label using just numbers from start of text field? Anonymous questions and Avatars Some Stack Exchange sites allow to ask an anonymous question by specifying a one-time user name and an email which is "required, but never shown". However the Gravatar attached to the email is shown anyway. Anonymous users do not want their picture to appear - someone can find their identity via google image search or someone that knows them.  Example: open incognito window and : Get string after character Bibliography tools that are compatible with biblatex and biber Parallel option performing worse on cluster I'm trying out oracles parallel option on a cluster and surprisingly I am getting worse results with the parallel option. I was expecting some improvement with the parallel option but certainly not worse results. I am wondering why this is the case, and if there is anything wrong with the way I am using the parallel option on my cluster.   I am using a degree of 4 when the number of CPU's I have is 8. I have tried adding parallel to the cluster directly ALTER CLUSTER cluster PARALLEL 4 as well as at the statement on both the index /*+ PARALLEL_INDEX(clust_index, 4) */and tables /*+ PARALLEL(4) */,   Here is my trace from the parallel:    Without parallel: Can someone remind me of the name of the author, the name of the hero and the name of the series if any? Adventure Sci-Fi books, short by today's epic standards ( = about same length as Heinlein's shorter youth books), probably published late 50s?, early 60s? by Bantam? or Del Rey? I think at least 30, possibly more than 40 books in the series. Not comic books. The author is not a well-known writer. At least, I don't remember seeing the name on any other books, ever.   Subject: a man who can move and respond to threats extremely fast learns about a secret potion that allows a person to change bodies with someone else and thus control them. A powerful organization does not want the secret to be known, because they use the potion to control politicians on many planets. The organization's goons are people who had surgeries to remove their emotions, and function like organic computers. They can communicate over interstellar distances and follow and murder anyone who learns the secret. I remember the following detail about the potion: there are two nearly identical molecules that have to be assembled in a certain sequence. Two of the components had to be switched around and that determined who would be dominant and who would be controlled during the mind switch / body swap.   Every book finds the hero on another planet with new adventures, and usually taking another deep-sleep-passage to another world, fleeing his pursuers. The background story about the secret potion is dished out little by little in each book.  One book in the series starts like this: hero is on very hot planet, diving for valuable marine life, catches a deadly fungus disease and is rescued last moment in exchange for his catch...  One of the themes that returns often is that the hero is an excellent knife fighter.  Of course he's a womanizer. In the second (or close to 2nd) book in the series, he's involved with a woman who rules a planet.  To travel to another world, he usually takes the cheapest dead-sleep passage, and there's always a 10-25% risk you won't wake up from that. How to prevent an email from accidentally being forwarded? As a new user without much rep, what should I do if someone else has already asked a question I have, but it has no answers? Buffering in meters/km using WGS84 layers using QGIS I am using QGIS 1.7.4-Wroclaw and working with an SHP layer in WGS84. I want to buffer out to a certain number of kilometers from this layer using the ftools buffer tool.  I understand that the buffer tool always uses the layer units, which for WGS84 are decimal degrees. We all know that degrees don't convert consistently to meters, so how should I go about making my buffers?   Is it necessary for me to convert the shapefiles to a different CRS that natively uses meters?   If so, how do I choose one? Who is the Lord, as referred to in the title? Frodo? Sauron? Someone else? Or is it more of an abstract title, not referring to a single person, like "He who wields the One Ring"? Maximum and minimum distance of two points Consider six distinct points in a plane. Let $m$ and $M$ denote respectively the minimum and the maximum distance between any pair of points.  Show that $M/m \geqslant \sqrt{3}$. How to show hidden folders in File Manager (Nautilus) on Ubuntu? Best practices for catching and re-throwing .NET exceptions I have a bunch of files as follows:  04602635_b0294.DAT20120807164534 04602637_b0297.DAT20120807164713 04602638_b0296.DAT20120807164637 04602639_b0299.DAT20120807164819 04602640_b0298.DAT20120807164748 04602641_b0300.DAT20120807164849 04602650_b0301.DAT20120807164921 04602652_b0302.DAT20120807164956   I need to rename them to exclude the prefix. It needs to look like this..  b0294.DAT20120807164534 b0297.DAT20120807164713 b0296.DAT20120807164637 b0299.DAT20120807164819 b0298.DAT20120807164748 b0300.DAT20120807164849 b0301.DAT20120807164921 b0302.DAT20120807164956   EDIT  I forgot to add that I am using Solaris. LED light needs replacing every few weeks I have two GU5.3 bulbs in my bathroom - one of them went off a month or so ago so I bought the following 3 pack:   I've gone through 2 of the new bulbs in the space of weeks. I have never seen the bulbs fade out while being on, it's only when we turn the light switch on that they don't come back on (like this morning, I was first in the bathroom and the bulb was off again). No fuses blown or any indication of tripping.  How should I approach this? Disable mouse speed check between monitors in windows 8.1 update 1 In windows 8.1 and below, the mouse would seamlessly move through all my monitors.  However, in windows 8.1 update 1 the mouse needs to be going at a certain speed before it goes to a different monitor. How do I disable this?  A google search has turned up nothing, so I'm not sure what exactly is going on How to manage a redirect request after a jQuery Ajax call Live USB for installation does not boot, black error screen followed by visual artifacts on a purple screen