Sharpshooter A hits the target 1/4 of the time. Sharpshooter B hits the target 2/5 of the time. If they both shoot, what is the probability that at least one sharpshooter will hit the target?
A coin is tossed three times. The probability of zero heads is 1/8 and the probability of zero tails is 1/8. What is the probability that there is at least one head and at least one tail?  So, if P(zero heads)= 1/8 , then that should be the same of p(all tails)?  We would use the complement rule and Multiplication Rule?   P(at least one head) = 1 - P(no heads) = 1 - 1/8= 7/8 P(at least one tail) = 1 - P(no tails) = 1 - 1/8= 7/8  would I multiply the two values?
This is a question from my proofs course review list that I have had trouble understanding.   I understand the concept of disjoint sets.  I'm not sure what they mean by countable. How would one prove a set is countable and furthermore, that the union of two countable sets is countable.  Please help me get started with the question by understanding this concept. When is it best to write "can't" versus writing "cannot"? Are they interchangeable in every situation? Games like Super Metroid and Aquaria present the terrain with the other facing parts having rocks and stuff while deeper behind them (i.e. underground) there's different detail or just black.      I would like to do something similar using polygons. Terrain is created in my current level as a set of overlapping square boxes. I'm not sure if this rendering method will work such a system for creating terrain but if anyone has ideas I'd love to hear them. Otherwise I'd like to know how I should re-write the terrain rendering system so it actually works to draw terrain in this manner... Finding $\int \frac{dx}{a+b \cos x}$ without Weierstrass substitution. I saw somewhere on Math Stack that there was a way of finding integrals in the form $$\int \frac{dx}{a+b \cos x}$$ without using Weierstrass substitution, which is the usual technique.   When $a,b=1$ we can just multiply the numerator and denominator by $1-\cos x$ and that solves the problem nicely.   But I remember that the technique I saw was a nice way of evaluating these even when $a,b\neq 1$. How to add keyboard shortcuts? Integral $\int_0^\infty \frac{\arctan(x) dx}{x(1+x^2)}$? How would one evaluate the integral $$\int_0^\infty \frac{\arctan(x) \,dx}{x(1+x^2)}$$?  I was told it had a nice closed form and could have been solved with differentiation under the integral sign; however, I tried to set $$I(\alpha) = \int_0^\infty \frac{\arctan(\alpha x) \,dx}{x(1+x^2)}$$ and got nowhere (the resulting integral was very messy). Is there a much more clever substitution that can be used to tackle the integral? "Be yet to do" vs "have yet to do" This theory has yet to be proven. This theory is yet to be proven. This is yet to be done. This has yet to be done. I have yet to spend summer in the mountains. I am yet to spend summer in the mountains.  Are they all correct? How are &quot;have yet to do&quot; and &quot;be yet to do&quot; different? Thank you! My program cannot run with "command not found" error I just switched from Windows to Ubuntu 11.10.  I wrote the following code in C with the text editor and saved it as HelloWorld.c in Documents.  #include &lt;stdio.h&gt; int main() {     printf("Hello World!\n");     return 0; }   And I started the Terminal and enter the following commands:  cd Documents  gcc HelloWorld.c   A file called a.out, which, after some search on Google, is the executable. I entered this command:  a.out   But I get   a.out: command not found   Which step did I do wrongly? Is there any shorter pronunciation of W than double-U? When spelling, every letter in the Alphabet is pronounced by a single syllable, with the only exception of W being pronounced "double-U". (Fun fact, in German it's approximately pronounced like the "ve" in very, but in some strike of cosmic justice Y is pronounced "Yps-e-lon") Why is that? Is there any at least semi-officially accepted one-syllable alternative pronunciation of W?  I checked some related post, e.g. , but they are more concerned with the "Why?" instead of the "Why not different?" Should the mean be used when data are skewed? Often introductory applied statistics texts distinguish the mean from the median (often in the the context of descriptive statistics and motivating the summarization of central tendency using the mean, median and mode) by explaining that the mean is sensitive to outliers in sample data and/or to skewed population distributions, and this is used as a justification for an assertion that the median is to be preferred when the data are not symmetrical.  For example:     The best measure of central tendency for a given set of data often depends on the way in which the values are distributed.... When data are not symmetric, the median is often the best measure of central tendency. Because the mean is sensitive to extreme observations, it is pulled in the direction of the outlying data values, and as a result might end up excessively inflated or excessively deflated."   —Pagano and Gauvreau, (2000) Principles of Biostatistics, 2nd ed. (P&amp;G were at hand, BTW, not singling them out per se.)   The authors define "central tendency" thus: "The most commonly investigated characteristic of a set of data is its center, or the point about which observations tend to cluster."  This strikes me as a less-than forthright way of saying only use the median, period, because only using the mean when the data/distributions are symmetrical is the same thing as saying only use the mean when it equals the median. Edit: whuber rightly points out that I am conflating robust measures of central tendency with the median. So it is important to keep in mind that I am discussing the specific framing of the arithmetic mean versus the median in introductory applied statistics (where, mode aside, other measures of central tendency are not motivated).  Rather than judging the utility of the mean by how much it departs from the behavior of the median, ought we not simply understand these as two different measures of centrality? In other words being sensitive to skewness is a feature of the mean. One could just as validly argue "well the median is no good because it is largely insensitive to skewness, so only use it when it equals the mean."  (The mode is quite sensibly not getting involved with this question.) If $x+{1\over x} = r $ then what is $x^3+{1\over x^3}$? If $$x+{1\over x} = r $$ then what is $$x^3+{1\over x^3}$$  Options: $(a) 3,$ $(b) 3r,$ $(c)r,$ $(d) 0$ I made a map with annotations in QGIS 3.0.  This is how it looks like in the layout view:    If I print the map as PDF, one would expect to get the PDF to be WYSIWYG, right? However, it looks like this (it's about half the size):    Is there a way to influence the the scaling of the Annoations? I already tried to play with the Scale and Magnifier in the map view. I also tried to change the Scale in the map item.   The strange thing is, I believe it worked a few days ago. But today I installed QGIS 3.0 on a new PC and it showed the same behaviour... Can a 20V 4.51A power supply be used with a computer that requires a 19V 3.42A power supply? How do you prove the set $G = \{(x, f(x)) \mid x \in \mathbb R\}$ is closed? Let $f : \mathbb R \to \mathbb R$ continuous. Prove that graph $G = \{(x, f(x)) \mid x \in \mathbb R\}$ is closed.  I'm a little confused on how to prove $G$ is closed. I get the general strategy is to show that every arbitrary convergent sequence in $G$ converges to a point in $G$.  Here is what I tried so far:   Let $x_k$ be a sequence which converges to $x$. Since $f$ is continuous, this implies that $f(x_k)$ converges to $f(x)$. At this point, can you say every $(x_k, f(x_k))$ converges to a $(x, f(x))$, so $G$ is closed? Permanently blocking a domain in iptables Suppose I want to block Facebook permanently. To do this, I have followed following processes:     #host -t a www.facebook.com   Sample output:     www.facebook.com has address 69.171.224.40   Find CIDR     #whois 69.171.224.40 | grep CIDR   Sample output:     CIDR:           69.171.224.0/19   To prevent outgoing access to www.facebook.com  Approach 1:     #iptables -I FORWARD -p tcp -d 69.171.224.0/19 -j DROP   Approach 2:     #iptables -I FORWARD -p tcp -d www.facebook.com -j DROP   Both Approaches work well. In approach 1, IP address may be changed so it will not block Facebook permanently. I don't know about approach 2 whether it will block Facebook permanently or not. If above approaches are not right way to block a domain permanently, how can I do it? How is being able to break into any Linux machine through grub2 secure? How is the ability of a person who gained physical access to your computer to get root with those steps in any way secure?   When grub2 menu opens press  e  to edit the Linux start options Change:   "linux   /vmlinuz-2.6.35-23-generic root=UUID=e7f1e48d-0015-485f-be7d-836217a31312 ro   quiet splash"    to:  "linux   /vmlinuz-2.6.35-23-generic root=UUID=e7f1e48d-0015-485f-be7d-836217a31312 ro init=/bin/bash"  Now you have root access just do:   mount -o remount,rw / passwd user mount -o remount,ro /  sync  reboot the computer and you win.   My question is, how is being able to break into any Linux machine through grub2 secure? I don't understand that fact about Linux, thank you for your answers. When and what cause Voldemort to look the way he does, vs how we've seen him as a teen? As the title says, when and what made Voldemort look the way he does (pale, snake-like etc) as opposed to how we've seen him in his earlier years as Tom Riddle? Is it just a side effect of his unnatural resurrection? Before he died attacking Harry as a baby did he look like a normal guy? network connection over thunderbolt bridge between linux and mac How do you set password-hash for OpenLDAP? Permission Denied To Delete File First of all, I'm not looking for an answer on how to remove the files. I am looking for a reason why this doesn't work - and a suggestion on how to remove the files without sudo.  I have a directory in my Desktop that has a few inner directories (don't judge the naming - I just extract what I need from files I'm given) and after getting the files I try and remove the files with rm -rf Bengal\ Tiger\ Creative/, I am surprised to see the following warning for each image.     rm: cannot remove ‘Bengal Tiger Creative/Bengal Tiger Creative/images/customer-services-landscape.jpg’: Permission denied   Below is some code outputs.  tree  nathan@nathan-pc:~/Desktop$ tree . ├── Bengal Tiger Creative │   └── Bengal Tiger Creative │       └── images │           ├── awards.jpg │           ├── blank.gif │           ├── bullet1-light-green.gif │           ├── bullet2-light-green.gif │           ├── bullet3-light-green.gif │           ├── bullet4-light-green.gif │           ├── customer-services-landscape.jpg │           ├── desktop.ini │           ├── header-img1.jpg │           ├── header-img2.jpg │           ├── header-img4.jpg │           ├── header-img5.jpg │           ├── softhr.gif │           ├── Thumbs.db │           ├── tiger_main-img1.jpg │           ├── tiger_main-img2.jpg │           ├── tiger_main-img3.jpg │           ├── tiger_main-img4.jpg │           ├── Vanquis-benefits-icons_iphone-green.gif │           └── white-arrow-green.gif   ls -laR  nathan@nathan-pc:~/Desktop$ ls -laR Bengal* Bengal Tiger Creative: total 12 drwxrwxr-x 3 nathan nathan 4096 Aug 10 11:30 . drwxr-xr-x 6 nathan nathan 4096 Aug 10 11:34 .. drwxrwxr-x 3 nathan nathan 4096 Aug 10 11:34 Bengal Tiger Creative  Bengal Tiger Creative/Bengal Tiger Creative: total 12 drwxrwxr-x 3 nathan nathan 4096 Aug 10 11:34 . drwxrwxr-x 3 nathan nathan 4096 Aug 10 11:30 .. dr-xr-xr-x 2 nathan nathan 4096 Aug 10 11:36 images  Bengal Tiger Creative/Bengal Tiger Creative/images: total 356 dr-xr-xr-x 2 nathan nathan   4096 Aug 10 11:36 . drwxrwxr-x 3 nathan nathan   4096 Aug 10 11:34 .. -rwxrwxrwx 1 nathan nathan  14910 Mar 18 12:29 awards.jpg -rw-rw-r-- 1 nathan nathan   1093 Mar 21  2014 blank.gif -rw-rw-r-- 1 nathan nathan   1978 May  8  2014 bullet1-light-green.gif -rw-rw-r-- 1 nathan nathan   1969 May  8  2014 bullet2-light-green.gif -rw-rw-r-- 1 nathan nathan   2416 May  8  2014 bullet3-light-green.gif -rw-rw-r-- 1 nathan nathan   2449 May  8  2014 bullet4-light-green.gif -rw-rw-r-- 1 nathan nathan 113138 Apr 14  2014 customer-services-landscape.jpg -r--r--r-- 1 nathan nathan    142 Mar 25 11:58 desktop.ini -rw-rw-r-- 1 nathan nathan  14312 Mar 23 11:39 header-img1.jpg -rw-rw-r-- 1 nathan nathan   1480 Mar 23 11:41 header-img2.jpg -rw-rw-r-- 1 nathan nathan   1278 Mar 23 11:41 header-img4.jpg -rw-rw-r-- 1 nathan nathan   1168 Mar 23 11:41 header-img5.jpg -rw-rw-r-- 1 nathan nathan   1703 Mar 21  2014 softhr.gif -rw-rw-r-- 1 nathan nathan  88064 Aug  4 10:39 Thumbs.db -rw-rw-r-- 1 nathan nathan  23607 Mar 23 11:56 tiger_main-img1.jpg -rw-rw-r-- 1 nathan nathan  23400 Mar 23 11:56 tiger_main-img2.jpg -rw-rw-r-- 1 nathan nathan   6970 Mar 23 11:56 tiger_main-img3.jpg -rw-rw-r-- 1 nathan nathan   8996 Mar 23 11:57 tiger_main-img4.jpg -rw-rw-r-- 1 nathan nathan    275 Jul 31  2014 Vanquis-benefits-icons_iphone-green.gif -rw-rw-r-- 1 nathan nathan   1821 Jul  9  2014 white-arrow-green.gif   Doing chmod 777 and then delete does not work.  Doing rm -rf * inside the directory does not work.  Doing sudo rm file does work.   I can easily remove these files using sudo, however, I cannot see why they cannot be removed without sudo. As a relatively new Ubuntu user, I would like to learn why.  Thanks in advance, Nathan