math forum
I got it! :3 That was easy. All you had to do is see what times itself is 26. AKA You just had to find the square root of 36. ->Math nerd<-
It showed up with the - sign on the top line and the 1 all by itself on the bottom line, so I thought it was asking the square root of 1
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This only holds true for a rectangle on a flat plane.
70.12 and 0.120.... in science the more 0's the better the answere because its more prisice
but the answer is correct. Perhaps word problems are such a lost art that feelingindifferent is unable to determine the implied brackets and the question does have value.
7-(4*13)+(17) = -28
multiplication and division before addition and subtraction. basic rules of mathematics, a child should know this.
Unless you state that there are brackets in the correct places then it is correct, but the question itself does not mention brackets so naturally it must follow the order - BIDMAS
Brackets, Indices, Division, Multiplication, Addition and Subtraction.
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8at first, i was totally convinced of aaron's analysis. but now i'm not. if the choices were only {BB GB GG}, that would lead to some pretty strange outcomes. for instance, if there were 4 kids, then the choices would be only {BBBB GGGG BBGG BGGG or GBBB}, giving equal probability to all four arrangements; but we know that the most-probable outcome should be 50%-50%. extend this to 100 kids, and you see the problem: it would be the same probability of having all boys as it would be to have a mixture of boys and girls. we know this is not right.
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so, the set {BB BG GB GG} is correct, because there's two ways of arranging a mixture, but only one way of arranging a pair. you can list the set as {BB BG GG} if you want, but you have to give a larger weighting to "BG" than the other two, because there's twice as many ways of arranging it.
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if you analyze this using a binomial distribution, it is more likely to get a family with at least one boy than it is to get a family with two girls (i.e. P(n=1 | 2) + P(n=2 | 2) = 1/2 + 1/4 = 3/4). i think that's the tricky part of the question. if you first exclude one outcome (GG), then you're left with three equally likely outcomes. two of those has a girl, so the probability is 2/3.
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another way to think about it: change the number of kids to 100. if you know that there is 1 girl in the family, what is the possibility that there is another child that is a boy. obviously, the probability is greater than 50%, because it's unlikely that all the 100 children are girls.
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but of course, if you ask what the chance that the next child born is a boy, the answer will always be 50%.
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if i'm wrong, what am i missing?I read through the entire explanation, and have concluded it is faulty logic, the explnation is simply confusing to the point that people will tend to accept it. Based upon simple genetics we know that the probability of any child being born a boy or a girl (assuming normal development) is 50%. If we already know what gender one child is that in no way affects the probability of the other's gender.
The logic from the explanation is wrong because it assumes a relationship between two completely independent events (unless the children are monozygotic twins...). For the first situation they list the possible permutations as BG, GB, BB, GG. This is incorrect, as each birth is independent, birth order has no relevence to probability. The actual permutations are BG(or GB, order is irrelevent), BB, GG. This still results in a 50% probability that the 2nd child will be a girl if the first is a boy. This means that the permutations for the 2nd question are BB and BG (or GB, but not both; order is still irrelevent). The probability is 50%.
The website you linked is just screwing with people's heads, and playing on our natural assumptions that birth order must in some way be relevent. Still a good question though, since it made me think, though you might want to say: "according to the boy or girl paradox..."
Furthermore... the author's brush off the idea of two BB combinations, which they cannot do based upon their assumptions that birth order is relevent. If we know one child is a boy, but not which one, AND we incorrectly assume birth order matters, we have:
BX or XB, depending whether it is the younger or older child being referred to in the question. Either X could be a boy or a girl, which results in 4 permutations, not 3. You must hold the B constant when determining the probability, which the authors of the "boy or girl paradox" did not. It's confusing to try and disprove confusing logic...Aaron is correct. This is a basic coin-flip argument in probability theory. The 1st result has NO EFFECT on the 2nd result. The chance of the 2nd child (or 3rd or 4th or 5th) is COMPLETELY INDEPENDENT of the result of the previous child. The given answer is wrong.
I refer you to my prob theory text book from undergrad:
Ross, Sheldon. "A First Course in Probability, 6th ed." Prentice Hall: Upper Saddle River, NJ. 2002. See Chapter 2: Axioms of Probability.
I'm sorry, I'm sure that this "Math Guy" from Stanford University is very smart, and I'm sure he knows more math than me, but I'm certain he is mistaken in this instance, if that post really is from him.
The real problem is that his proof does not hold a constant assumption. He assumes birth order doesn't matter if there are two male siblings, but that it does matter if there is one male and one female sibling. He has to have a constant assumption for the logic to work. If this doesn't convince you, we can demonstrate that the 2/3 probability is not accurate scientifically:
Based upon this paradox, we would make the hypothesis that in any family in which at least one of two children is a boy, there is a 66% chance that the other child is a girl. We can check sensus data to test this hypothesis. I don't want to spend the time doing that right now, but I am confident this hypothesis will not hold up to such an investigation.
As clever as any argument is, if the data doesn't hold up to scientific investigation, one must concede it is flawed.
The wikipedia site fails to hold its assumptions constant as well (it wasn't loading earlier). It blatantly contradicts itself with a careful reading. It first says "Neither order nor age is important.", and then later disregards this in saying that it matters whether the sister is older or younger (but not the brother).
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The math tag kinda gives it away.
good thing i have it selected for math lol
Good Will Hunting
F. yeah I cam here to say that ^_^
*came