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 Jun 4 awarded Yearling Mar 19 answered Irrational diagonal length problem. Jan 23 answered Does every ball of boundary point contain both interior and exterir points? Jan 8 answered Solving for two variables in terms of two other variables Sep 25 comment Prove that $2^{1/2}$ is irrational When you have more than one assumption and you reach a contradiction, you need a way to determine which assumption is incorrect, since failure of any of them (or all of them!) could have led to the contradiction. That gets tricky, so we try to avoid it in general. The only good way I know of to disprove an assumption when you have multiple assumptions snarled together is to show that one of the assumptions causes a contradiction no matter how you choose the others. Sep 25 comment Are “proofs” that are contingent upon physical reality valid? Sorry, but what does "touches the side within P" mean? Sep 25 answered Prove that $2^{1/2}$ is irrational Sep 23 comment Conditional probability of picking particular second letters in Scrabble, given the first letter picked Unfortunately, unless a question is posed using rigorous mathematical language, you're forced to interpret in context. As always with word problems, this takes practice so try to encounter as many of these as you can. In this instance, the question specifically refers to things happening first, then second. That's a red flag that you're nearing conditional probability land. If you determine that different outcomes for the first event change the probabilities for the second (in this case picking or not picking a D or K 1st changes your 2nd outcomes), then you're dealing with conditional probs. Sep 18 comment Conditional probability of picking particular second letters in Scrabble, given the first letter picked Unfortunately, they're not equal, because B and A aren't independent. That equation only holds when $P(A\cap B) = P(A)\times P(B)$, which is only true if they're independent. en.wikipedia.org/wiki/Independence_(probability_theory) Sep 18 answered Conditional probability of picking particular second letters in Scrabble, given the first letter picked Sep 18 comment Conditional probability of picking particular second letters in Scrabble, given the first letter picked If I chose with replacement, then the chance of pulling a D or a K on the second draw would be 2/7, regardless of the first draw. As it stands, the "Correct" answer looks wrong to me. I'll post an answer an explain... Sep 17 comment Conditional probability of picking particular second letters in Scrabble, given the first letter picked The only way I get their answer is if the picking is done with replacement (which seems unlikely given what I know of Scrabble). Did they mention that in the original question? Sep 10 answered Why can't equations with unknown inside and outside of a function be solved in a standard way? Aug 19 answered How fast does a sequence with finite sum go to zero? Aug 8 comment Determine ellipse from two points and direction vectors at those points Right, sorry. Spaced out because the points aren't marked in the figure. (Don't do math before caffeine.) Aug 8 comment Determine ellipse from two points and direction vectors at those points To see a few of the infinitely many possible ellipses, imagine the ellipse in your picture. Now shrink it to half the size, then push it up until it hits your tangent lines. In fact, any ellipse of any size and orientation can be translocated until it touches those lines in exactly 1 point each. (Better yet, imagine flipping your picture over and dropping an ellipse into the top. It would roll/slide/fall until it rested on tangents against the lines.) Aug 7 comment Show an equation of a line passing through $P$ and parallel to the line given by $ax+by+c=0$. If both $a=0$ and $b=0$, then the equation $ax+by+c=0$ reduces to $c=0$, which is not the equation of a line. If $c=0$, then it's the whole plane, because any point $(x,y)$ satisfies it. If $c\neq0$, then it's an empty set of points. Including $a^2 + b^2 \neq 0$ in the question just rules out the case where both are $0$, so that all you're left with are valid linear equations. Aug 5 answered Proof that for any n-sided polygon P, and any integer m greater than n, there is an m-sided polygon with the same area and perimeter as P? Jul 21 comment Can you show me where the “1/2” comes from? +1. The color is a nice touch. Jul 21 comment probability problem explanation +1, and thanks for the head's up on my answer. Looks like I misread the OP due to typos. Will probably remove my answer so as not to cause confusion.