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Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
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The only one I've gotten so far was the letters/numbers card problem. The probability stuff is over my head. I usually sort of get it when it is explained, but I still don't understand why, for example, the sperm & egg of the second child would care what the gender of the first child was. It still seems like it should be 50/50 to me, although I can follow the reasoning in the solution.
The one who buggers a fire burns his penis
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“Pleasure to me is wonder—the unexplored, the unexpected, the thing that is hidden and the changeless thing that lurks behind superficial mutability. To trace the remote in the immediate; the eternal in the ephemeral; the past in the present; the infinite in the finite; these are to me the springs of delight and beauty.” ~ H.P. Lovecraft
The trip up for this one is that it doesn't say whether the boy (or girl if the question is asked that way.) is the first or second child. It gets read as "If the first child is a boy, the second child has a ...chance to be a girl", but is really, if either the first or second child is a boy, the other child has a ... chance of being a girl."
The one who buggers a fire burns his penis
-anonymous graffiti in the basilica at Pompeii
It took me a second to parse the question... The way I ended up rephrasing the question...
Given that one of the two kids will be a boy, what is the chance that there will also be a girl? The solution lists all the possible situation, eliminate the one that doesn't apply... and the solution comes from that. That's the mental gymnastics I did, anyway - it took me a bit to figure out what was being asked. For some reason I kept reading it as "The first child is a boy, what are the chances the second child is a girl" which isn't the same thing.
On one side I had a "previous flips do not matter" rule pounding in my head and I had to beat it into submission before I could even read the problem properly. Funny enough I probably would of been able to do it with a different context easier... I have children = "previous flips do not matter!" etched in my brain.
Yes Jennifer that is correct, and I actually appreciate the non-mathese explanations, like the one you gave, whenever they are possible.
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Okay, then let's look at a slightly different problem along the same lines:
"My neighbor has two children. What is the probability that one of them is a girl?"
How would you parse this, then?
It depends if you mean "at least one is a girl" or "exactly one is a girl". In a math context a person would generally assume that you mean "at least one is a girl".
If a person has 2 children then there are four possibilities: BB, BG, GB, GG.
So the answer is either 3/4 or 2/4=1/2 depending on what you mean.
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