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  1. #111
    filling some space UnitOfPopulation's Avatar
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    Quote Originally Posted by The_Liquid_Laser View Post
    (The problem below assumes that when a woman gives birth there is an equal chance of the child being either a boy or a girl.)

    My neighbor has two children. One of them is a boy. What is the probability that the other child is a girl?
    Solution..
    For combinations of 1st and 2nd child, we have
    p(BB) = p(BG) = p(GB) = p(GG) = .25

    those including boys have X = p(BB or BG or GB) = .75
    and of those including girls Y = p(BG or GB) = .5,
    and the probability is given by Y/X = 2/3.


  2. #112
    Glowy Goopy Goodness The_Liquid_Laser's Avatar
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    Yes Santtu that is correct.
    My wife and I made a game to teach kids about nutrition. Please try our game and vote for us to win. (Voting period: July 14 - August 14)
    http://www.revoltingvegetables.com

  3. #113
    filling some space UnitOfPopulation's Avatar
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    Quote Originally Posted by athenian200 View Post
    I really think only an IxTP could just accept logic like that without an inner struggle (that's their primary strength).
    Well with doing few mathematical exercises, you could probably catch on fast. After a while, it's easy to recognize when some statement is given in the language of mathematics. Usually the whole situation is then completely described in the statement given and no outside influences are allowed, except for knowing how to calculate, of course.

    It doesn't mean that mathematicians wouldn't care about the real life! It's just that it's impossible to transfer the whole world to the language of mathematics with all it's nuances. That's why the world is there, to be lived and experienced. Using mathematics, one is bound to consider only limited aspects of it an any one time, or the problem would be ill-defined. I believe that mathematicians are often extremely interested of the applied parts, i.e. where the theory meets the world. Sometimes some concepts are generated more for the mathematical community rather than for the public.

    One analogy could be that of business-to-business sales and selling to consumers: both are needed.

    In short, mathematics is for well-defined problems, but humans excel in ill-defined problems. There's also interesting mixes of the two such as recommendation systems, neural nets, pattern recognition etc.. the methods may be strict, but in the end, it's the human who judges how well a problem is really solved.

  4. #114

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    Quote Originally Posted by The_Liquid_Laser View Post
    No the answer is not 1/2. I can assure you that the problem I'm presenting is not equivalent to the one you are describing with coin flips.
    Even here, interpreting the problem statement is where a lot of the problem lies.

    Some people may interpret the problem to mean that your neighbor is about to have a second child (a misinterpretation, but seems to be common), instead of already having two children.

    I guess Santtu already posted the spoiler, but I have always been fascinated by how people make mistakes. It would have been interesting to see what other answers people came up with.

    Accept the past. Live for the present. Look forward to the future.
    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
    "[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

  5. #115
    filling some space UnitOfPopulation's Avatar
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    Quote Originally Posted by ygolo View Post
    I guess Santtu already posted the spoiler,
    Sorry, was the answer too visible? I tried to select a color that would blend into the background.

  6. #116

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    Quote Originally Posted by Santtu View Post
    Sorry, was the answer too visible? I tried to select a color that would blend into the background.
    I think it's fine. I personally find white harder to read, w/o highlighting.

    Accept the past. Live for the present. Look forward to the future.
    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
    "[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

  7. #117
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    Quote Originally Posted by The_Liquid_Laser View Post
    No the answer is not 1/2. I can assure you that the problem I'm presenting is not equivalent to the one you are describing with coin flips.
    Thanks. I read Santtu's answer...this is fascinating stuff.

  8. #118
    Protocol Droid Athenian200's Avatar
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    Darn, I haven't gotten any of these right... I've only managed to make myself feel stupid. I must be the thickest person here. I just don't think this way, there's too many variables, and too many specific technicalities and rules that affect the answer that aren't immediately apparent. How do you manage to think like this? You'd have to be a rocket scientist.

  9. #119
    Glowy Goopy Goodness The_Liquid_Laser's Avatar
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    Quote Originally Posted by ygolo View Post
    Even here, interpreting the problem statement is where a lot of the problem lies.

    Some people may interpret the problem to mean that your neighbor is about to have a second child (a misinterpretation, but seems to be common), instead of already having two children.

    I guess Santtu already posted the spoiler, but I have always been fascinated by how people make mistakes. It would have been interesting to see what other answers people came up with.
    This is what I said. "My neighbor has two children. One of them is a boy. What is the probability that the other child is a girl?"

    I admit it's easy to misinterpret a problem the first time it is read, but I don't think the wording is unclear. Isn't it clear that the neighbor already has two children?
    My wife and I made a game to teach kids about nutrition. Please try our game and vote for us to win. (Voting period: July 14 - August 14)
    http://www.revoltingvegetables.com

  10. #120

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    Quote Originally Posted by athenian200 View Post
    Darn, I haven't gotten any of these right... I've only managed to make myself feel stupid. I must be the thickest person here. I just don't think this way, there's too many variables, and too many specific technicalities and rules that affect the answer that aren't immediately apparent. How do you manage to think like this? You'd have to be a rocket scientist.
    A lot of these problems have success rates of 1 in 10 or something, despite the initial appearance of being "simple".

    I didn't get the Monty Hall problem the 1st time I saw it, either.

    But the basic idea to understand is Conditional Probability.

    Besides that the way to think about a probability problem is to imagine running a whole bunch of "experiments" of the problem statement in parallel, chosing the parameters according to known probability distributions.

    I may post something more detailed after work (unless someone beats me to it) or if I have some down time. I've been really busy today.

    Accept the past. Live for the present. Look forward to the future.
    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
    "[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

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