A family has two children. What is the probability that both the children are boys given that at least on of them is a boy?  Solution given in my book is    My doubts and my solution  If a family has a child and you are required to find that what is the probability of it to be a boy then your answer will be 1/2.  Now in the present problem it is given that out of two children one is a boy then what is the probability that both are boys.  One child is boy the second child can be a boy or a girl, chance of boy is 1/2.  $P(boy|boy)=\frac{1}{2}$  What I mean is that there are two possible outcomes after we have a boy, it can be a boy or a girl out of this boy is a favorable outcome and so we have 1/2.  Request  Please don't mark this problem as duplicate of  or of  because my logics are different.
In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?  I just dipped into a book, The Drunkard's Walk - How Randomness Rules Our Lives, by Leonard Mlodinow, Vintage Books, 2008. On p.107 Mlodinow says the chances are 1 in 3.   It seems obvious to me that the chances are 1 in 2. Am I correct? Is this not exactly analogous to having a bowl with an infinite number of marbles, half black and half red? Without looking I draw out a black marble. The probability of the second marble I draw being black is 1/2.
I'm trying to make a basic Windows application that builds a string out of user input and then adds it to the clipboard. How do I copy a string to the clipboard using Python? Why Did Anakin Skywalker Believe that Turning to the Dark Side of the Force Would Save Padmé? Just as the question asks: Why did Anakin come to believe that Padmé could be saved if he embraced the Dark side of the Force? Padmé clearly didn't believe it. Why was Anakin so driven to save Padmé through the dark side? Can virtual particles be thought of as off-shell Fourier components of a field? I just found  blog post, which gives an interpretation of virtual particles I haven't seen before.  Consider a 1D system of springs and masses, where the springs are slightly nonlinear. A "real particle" is a regular $\cos(kx-\omega t)$ wavepacket moving through the line, where $\omega$ satisfies the dispersion relation $\omega = \omega(k)$. When two real particles collide, the region where they collide temporarily looks really weird, as they interact nonlinearly, pulling and pushing on each other.  Formally, we can write this weird region as the sum of a bunch of $\cos(kx-\omega t)$ waves, but there's no guarantee they'll have the right dispersion relation. Thus, each term in the resulting expansion is a off-shell "virtual particle". If you add up all the virtual particles, you get the actual intermediate field state, which is just a weird ripple in the field where the two particles are interacting.  As another example, consider the statement "a static EM field is made of virtual particles". Under this interpretation, what that really means is, "a static field (e.g. $1/r^2$) is not equal to $\cos(kx-\omega t)$, but may be expanded in terms of such sinusoids", which is much less mysterious sounding. In fact, this is exactly what we do when we consider scattering off a potential in normal QM, e.g. in the Born approximation.  The above gives some intuition for what a 'virtual particle' means in classical field theory. They are the Fourier components of the field with $(\omega, k)$ not satisfying the dispersion relation, and they are useful in classical perturbation theory. However, they are not propagating degrees of freedom, so they only appear during interactions.   The picture above is entirely classical. Does this picture generalize to quantum field theory, giving a physical intuition for virtual particles there? set fontsize for TikZ figure I have made many figures with tikz and want to include them in a template. Unfortunately I used ex as a measure and the template I have to use redefines the font size. THis leads to wrong distances in the figures. is there a way to set the font size for all tikz figures in a document, so I do not have to adjust my figures? I already know how to do it on Mac OS X (plenty of instructions online).  But is it possible to do it on Ubuntu? If yes, how? Limit of Series with differences of Floor function Why did the Star Trek writers decide Warp 10 would be infinite? From  onward,  has a basically cubic scale from warps 1 - 9. But then, close to warp 10, it suddenly develops its own puzzling scale, as can be seen in .  In this scale, , occupying all points in the universe simultaneously and therefore effectively teleporting instantaneously.  My question is why have this confusing scale? Why not have a uniform cubic scale? Was there ever any "official" explanation for this?  Clarification: I'm looking for why the writers decided on this, not the "in-universe" explanation. I have created my StackOverflow Careers panel, and when I click 'add a stack overflow account with over 200 reputation' the site decides that I have no StackOverflow account at all, although my current one has over 300. I log in to both with the same StackExchange Account with the same email etc so I'm curious as to why this is happening. Create model from XYZ data points I'm trying to create a 3D heat map model out of data that I have from a csv file. I have a few thousand data points with XYZ coordinates.  I'm able to import the data into blender as a point cloud with , however I would like to create a model with solid faces. Is there a way when importing the data to somehow join the points to create faces instead of generating thousands of separate points?  Currently, this what I have in terms of point cloud  The end product would look something like this (minus the texture) and obviously the model wouldn't be as regular as this one  Any help is greatly appreciated! Is $f(a)\!=\!0\!=\!f(b)\Rightarrow (x\!-\!a)(x\!-\!b)\mid f(x)\,$ true if $\,a=b?\ $ [Double Factor Theorem] How do I get the title of a .pdf document to appear as the page title? Installing older iOS for device testing Showing that $\lim_{x \to 1} \left(\frac{23}{1-x^{23}}-\frac{11}{1-x^{11}} \right)=6$ How to add a custom action to the list ribbon? How to add a custom action to the list ribbon?  The custom action should open a sitepage in modal popup. How to apply multiple styles in WPF In WPF, how would I apply multiple styles to a FrameworkElement?  For instance, I have a control which already has a style.  I also have a separate style which I would like to add to it without blowing away the first one.  The styles have different TargetTypes, so I can't just extend one with the other. QGIS 3.0 and Qt 5.7 time schedule When will QGIS 3.0 with QT5.7 (possibly) be released as a stable and long term support version? Dirac's remark that inspired Feynman when formulating path integral When Feynman was trying to formulate  of quantum mechanics, he was inspired by Dirac's remark which roughly states that $e^{i\frac{S}{\hbar}}$corresponds to the transition amplitude, where $S$ is the action.   I'm wondering what was Dirac's original argument behind this statement. Is the following sentence correct English?      Have you the address?   The address in question is obvious to the person being asked.  It's normal to ask such a question as "Do you have the address?" or even "Have you got the address?" But is it acceptable to use just the verb have without do or got? how to get the selected date in jquery I have 2 HDD drives in my computer. At the moment second drive is mounted as /media/storage.  How can I move my user data from /home to /media/storage/home?  Can I just move the data over there and then simply symlink it back?