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Apr 17 |
comment |
Probability by throwing a tetrahedron $P(A\cap B)$ is the fraction of them that count as examples of both condition $A$ and $B$. The only ones satisfying this are $(3,3)$ and $(4,4)$, giving a probability of $2/16=1/8$. Keep in mind that since this is more restrictive than requiring $A$ or $B$ by themselves, $P(A\cap B)$ can't be larger than $P(A)$ or $P(B)$. The logic for $P(A/B)=\frac{P(A\cap B)}{P(B)}$ was good though. To calculate $P(A\cap B)$ you could also just look at the things that satisfy $B: (2,4),(3,3),(3,4),(4,2),(4,3),(4,4)$, and see what fraction of them also satisfy $A$. |
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Apr 17 |
comment |
Probability by throwing a tetrahedron $A$ contains the ones where you got the same number twice. $(1,1)$ does this, since that means you got a one on the bottom both times. $(1,2)$ doesn't, since you didn't get the same number on both throws. |
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Apr 17 |
answered | Probability by throwing a tetrahedron |
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Apr 17 |
answered | Strange behavior of $\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}$ |
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Apr 16 |
comment |
Is there a problem in studying analysis before calculus? Spivak is an excellent "middle of the road" book. I would like to point out that calculus is only enriched by its numerous applications; they aren't merely some sort of baggage to be avoided. While there may not be a problem with skipping it, I wouldn't go so far as to avoid the 'calculation and application' side of things completely. |
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Apr 14 |
answered | Why can't you add terms with different exponents? |
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Apr 12 |
comment |
What is the official proof (if there is any) for the area of a circle of radius 'r'? do you have some other definition for $\pi$? Or is this asking why it should be proportional to $r^2$ in the first place? |
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Apr 11 |
awarded | Yearling |
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Apr 7 |
awarded | Guru |
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Apr 6 |
comment |
My approach to a CFG Thanks! I'd wait a bit before you accept the answer though; you might get some more comments from people who know the area far better than me if you leave it open for a while. |
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Apr 6 |
answered | My approach to a CFG |
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Apr 5 |
awarded | Good Answer |
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Apr 5 |
awarded | Nice Answer |
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Apr 5 |
answered | Do factorials really grow faster than exponential functions? |
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Apr 4 |
answered | Clues to find the graphs of functions |
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Apr 3 |
answered | Larger Theory for root formula |
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Apr 2 |
answered | I need a differentiable function whose plot is a plateau and the steepness and width can be varied arbitrarily and easily |
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Apr 2 |
comment |
How often does it happen that the oldest person alive dies? Don't you need more information than this? "everyone lives forever" satisfies the criteria in your question, and then you're never notified. If this were a mayfly population there would be multiple notices in a minute. What are we taking as the average lifespan? |
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Mar 30 |
awarded | Nice Answer |
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Mar 28 |
revised |
How can one prove that $\lim\limits_{\theta\to 0} \frac{\sin\theta}{\theta}=1$ added 552 characters in body |
