J.R.
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 Mar 8 comment Probability of picking 4 red balls As an aside, this problem could be reworded as: "There are 11 balls in a jar, numbered 1-11. You pick out four balls at random. What is the probability that all four balls will be odd numbers?" Mar 8 comment Probability of picking 4 red balls @Tejus - The only way the numbers would be different by selecting the balls one-at-a-time would be if the selected balls were returned to the bin after each pick. If they are kept out of the hopper, though, then it makes no difference if you pull them out one at a time, or all at once. May 19 awarded Citizen Patrol May 19 comment If you draw two cards, what is the probability that the second card is a queen? @Tony - If the first card is an ace, then it is less likely that the 2nd card is an ace. From a card player's perspective, that's true. But, what happens when the first card is not an ace? Then, it is more likely that the second card is an ace. 1/13th of the time the probability will go down, while 12/13ths of the time the probability will go up. In the end, the numbers cancel out, and we're back to 1/13th. A.J.'s answer has the actual values. Feb 22 comment Visually stunning math concepts which are easy to explain @Peter - I'll admit that I'm using the word derive a bit loosely for a mathematics forum (it's a soft answer to a soft question), but it's too bad you see this as "dumbing down" and "a waste of time." Most 7th-grade teachers charged with teaching volume would simply write the formula on the board, and it would be well-forgotten by the end of summer. Her technique might have been weak insofar as mathematical rigor goes, but the pedagogy was very strong. I assure you, this woman was not one to "dumb down" anything; I remember re-learning concepts in 11th-grade that she taught us in Jr High. Feb 15 awarded Great Answer Dec 19 awarded Constituent Dec 15 awarded Caucus Oct 19 comment Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist? RE: "I think there is only one infinity, we can think it as the biggest number..." You might want to get a better grasp on what infinity means; there is no "biggest number." Incidentally, a better way to phrase your title would be to refer to the string of 0's as infinitely many zeroes, not an infinite number of zeroes. Sep 24 awarded Autobiographer Aug 28 comment Visually stunning math concepts which are easy to explain @DanielM - You're right, the experiment isn't a proof. Then again, neither is the formula. I just wanted to draw attention to how my math teacher's technique left a lasting impression that the formula by itself could never manage to do. Apr 22 revised If there are obvious things, why should we prove them? deleted 1 character in body Apr 20 answered If there are obvious things, why should we prove them? Apr 20 comment If there are obvious things, why should we prove them? Not my downvote, either, but: Immoral? Sacred? For someone professing such strict adherence to rigor, those words are a bit over-the-top. Apr 20 comment Are there 3 trig functions or are there 6 trig functions? The bottom line answer always seems to be "it depends." Great link, btw. Apr 13 comment Visually stunning math concepts which are easy to explain @Travis - That's why I gave up and constructed my own image. (Hopefully one that illustrates my point a little better.) I left the other image in my answer so as not to render all these comments obsolete. Apr 13 awarded Editor Apr 13 revised Visually stunning math concepts which are easy to explain added 411 characters in body Apr 13 comment Visually stunning math concepts which are easy to explain @Travis - Yes, a few folks have made that observation. Perhaps I didn't choose the best examples. I'll stand by my point, though: diagrams showing little more than a polygon, some labels, and an equation often lead a student toward a plug-and-chug mindset that isn't as instructive as it could be. I still think first diagram has plenty of room for improvement; it could be drawn in a way that would do a better job of nudging a student toward your line of reasoning. Apr 7 awarded Good Answer