Probability number A greater number B Given $a \in \{1,2,...,250\}$ and $b \in \{0,1,...,1000\}$  $a$ and $b$ are chosen randomly, how does one calculate the probability of $a &gt; b$?
Probability Number A greater Number B Given $a \in \{1,2,...,250\}$ and $b\in \{0,1,...,1000\}$  What is the probability that $a &gt; b$?  I know there already is  question with a very similar question, however it's over an interval of $\mathbb{R}$ so I hope there is another way opposed to the Integral used in the formal solution.  How does one go about calculating said probability?
says that the number of different monomials of degree $M$ in $N$ variables is $$\frac{(M+N-1)!}{M!(N-1)!}\; .$$ Can anyone explain why this is true? So I defeated a Team Valor gym earlier today using my highest cp Pidgeot. It turned grey, so I went to claim it with that Pidgeot, except it wouldn't let me. What determines which pokemon you are allowed to place at a gym? Is it just those who have participated in a battle can't? Is there a time period for it? What about training at a friendly gym? Does this impact anything? Does D&D 5e have a rule for character knowledge about monsters? In the 3rd and 4th editions of D&amp;D, there were explicit rules for determining if a character knew anything about a monster before them.  In 3rd edition, for example, use of the  skill with a general DC of 10 + the monster's HD allowed for determining one fact, plus one fact per 5 points over the check.  Looking at the Intelligence section of the 5e PHB, I don't see any similar notation.  Does 5e provide any guidance as to when a player could use their out-of-game knowledge about a monster, or when the player might be told things their character would probably know in-game? Apple Macbook Dual Monitor MST Programmatically disable apt unattended upgrades How can I programmatically/script disable apt unattended upgrades? Running Ubuntu 16.04. Multiple Inheritance in C# What is scientific mind? How can you define scientific mind? What i think , it is a bend of mind that can be developed by any person(also one not related to field of science).This mind is fulfilled with abilities to observe clearly and sceptical about what he sees.It means the person will be keen to dig out truth and did not reaches to a conclusion easily. He utilizes facts enhance them with logical reasoning and fills the gap with their imagination.  Is there any disadvantage or any kind of limitation with scientific mind? This issue came up when I got different records counts for what I thought were identical queries one using a not in where constraint and the other a left join. The table in the not in constraint had one null value (bad data) which caused that query to return a count of 0 records. I sort of understand why but I could use some help fully grasping the concept.  To state it simply, why does query A return a result but B doesn't?  A: select 'true' where 3 in (1, 2, 3, null) B: select 'true' where 3 not in (1, 2, null)   This was on SQL Server 2005. I also found that calling set ansi_nulls off causes B to return a result. DDL Trigger in MySQL? When trying to SSH into a particular Mac machine it gives me the following error :  ssh_exchange_identification: Connection closed by remote host   I have done some google searches on the issue but I haven't seem to find a definite answer. I did notice that on the machine that I am trying to SSH into, it does not have the ~/.ssh file even on there so I went ahead and created it and gave it correct permissions but that didn't help. Here is the verbose of when attempting to SSH into it:  penSSH_6.2p2, OSSLShim 0.9.8r 8 Dec 2011 debug1: Reading configuration data /etc/ssh_config debug1: /etc/ssh_config line 20: Applying options for * debug1: Connecting to &lt;ComputerName&gt; [xxx.xxx.xxx.xxx] port 22. debug1: Connection established. debug1: identity file /Users/&lt;UserName&gt;/.ssh/id_rsa type 1 debug1: identity file /Users/&lt;UserName&gt;/.ssh/id_rsa-cert type -1 debug1: identity file /Users/&lt;UserName&gt;/.ssh/id_dsa type -1 debug1: identity file /Users/&lt;UserName&gt;/.ssh/id_dsa-cert type -1 debug1: Enabling compatibility mode for protocol 2.0 debug1: Local version string SSH-2.0-OpenSSH_6.2 ssh_exchange_identification: Connection closed by remote host   Any ideas on how to get SSH working? $(m, m+2)$ is twin prime, iff $4((m-1)! + 1) \equiv -m \pmod {m(m+2)}$ The Wiki page on  says     The pair $(m, m+2)$ is twin prime, iff $4((m-1)! + 1) \equiv -m \pmod {m(m+2)}$.   This is obviously connected to Wilson's Theorem. Can anybody provide a proof for that, along the lines of thought given here, ? Where did the age go on the network profile? Ever since the profile redo, the age was shown in the network profile, but not in the per-site profiles. So if someone wanted to see the age, they had to go to the network profile. However.. It's vanished! The field is still there in the profile editing, however. It doesn't appear as if this was implemented:   So... Where is it? How to grep a specific line _and_ the first line of a file? Assuming a simple grep such as:  $ psa aux | grep someApp 1000     11634 51.2  0.1  32824  9112 pts/1    SN+  13:24   7:49 someApp   This provides much information, but as the first line of the ps command is missing there is no context for the info. I would prefer that the first line of ps be shown as well:  $ psa aux | someMagic someApp USER       PID %CPU %MEM    VSZ   RSS TTY      STAT START   TIME COMMAND 1000     11634 51.2  0.1  32824  9112 pts/1    SN+  13:24   7:49 someApp   Of course, I could add a regex to grep specifically for ps:  $ ps aux | grep -E "COMMAND|someApp"   However, I would prefer a more general solution as there are other cases in which I would like to have the first line as well.  Seems like this would be a good use case for . In the simple linear regression model, $\hat{\beta}$ is the sum of independent normally distributed random variables.  Is it false because in linear regression there is $\beta$ and not $\hat{\beta}$? Route SSH to host through interface Is it possible to route all outgoing requests for SSH (port 22) to mydynamicdns.afraid.org via wlan0 instead of eth0 when both are connected?  Since my IP is dynamic, I would like to use a name instead of IP. Complex number operations: telling Mathematica variables are real How can i check if $remote_addr IP is NOT in CIDR range in nginx? I am using nginx latest web server. How can i check if the $remote_addr ip is NOT in specified CIDR range and return appropriate error code.  i would like to return specific error codes if IP is NOT in specific CIDR IP ranges.  how can i do this for CIDR IP range ?  e.g.    If remote_addr is not in 123.123.123.123/24 then return 444 code . How do I make a 2D game resolution independent? I'm working on a simple 2D game. I've finished the mobile phone version.  However, my boss wants the game to works on his RT. I'm doing the "conversion" but my buttons are in the wrong places, because I hard-coded the screen size, like this:   texture = game.Content.Load&lt;Texture2D&gt;("StartScreen");  mainFrame = new Rectangle(0, 0, game.GraphicsDevice.Viewport.Width, game.GraphicsDevice.Viewport.Height);   // button definitions  startbrect = new Rectangle(300, 258, 88, 88);  startbtext = game.Content.Load&lt;Texture2D&gt;("bplay");   In this example, mainframe is fine, but startbrect isn't, because I defined the size to match a Windows phone's screen. How can I handle responsive design when all Windows 8 phones' screens are different? Is there a formula or macro to calculate each time the good size? Why is this command not working: "ps aux | grep xscreensaver" I didn't see any hits about this on google, so I'm asking you:  I just tried to run this command in an ssh session, local is Debian Wheezy KDE, remote is Fedora 21 Gnome:  ps aux | grep xscreensaver   and this is the output:  bash:  grep: command not found...   I never seen this before, what is the cause?  I just few hours before updated the system, but didn't see any packages marked for removal. There are only two users on the system, and only me installs or removes software on it.  EDIT #1  Here is the commands and output copied,notice that the space is not there the second time:  [root@Hostname ~]# ps aux |  grep xscreensaver bash:  : command not found... [root@Hostname ~]# ps aux | grep xscreensaver bash:  grep: command not found... Everyone I speak to says that a 50mm lens is the best and beats them all as an all-rounder. I was wondering whether to get myself a decent, fast 50mm as well. However I'm still not 100% sure whether I really need such a lens.  I use a Pentax K10D and mainly shoot people (kids, portraits, some street shots). The lens I love and use most is the DA 70mm f/2.4 Limited. I often also use a DA 40mm f/2.8 Limited. They are great little lenses that produce very high quality images but they could be a bit faster.  Is is worth spending 400 quid on a Sigma 50mm f/1.4 in my situation? It seems like a good compromise between the 40mm and 70mm and much faster (in fact, 2 f-stops faster than the DA 70mm f/2.8!). On the other hand would the lens be sufficiently different from my current lenses?