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Just a general probablility question

  1. Feb 6, 2005 #1
    this is what got me thinking....it might be a bit dumb, but.....uh...yea.

    haha.

    ok, so given a fair coin, there is 1/2 chance to get heads or tail when tossed. since each toss in the air is independent, there is always 1/2 chance.

    so if you set up some kind of system to flip the coin, everytime the coin is tossed, it is tossed the same way, i.e, same speed, spin, hight, same landing....basically, it is just tossed the exact same way, and there is no human error or anything.

    so if I toss it 10x, will it get 5 heads and 5 tails? and will I toss 100x, will it get 50 and 50.

    So what i'm asking is, whenever they say something has a 50% chance, when you do your experiement the absolutly same way every single time, will it always be exactly a 50/50 split?

    maybe a dumb question, but just wondering....
     
  2. jcsd
  3. Feb 6, 2005 #2

    Hurkyl

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    What if you toss it 9 times?
     
  4. Feb 7, 2005 #3

    mathman

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    The results of tossing a fair coin n times is given by the binomial distribution. Specifically the probability of k heads is n!/(k!(n-k)!2n).
     
  5. Feb 7, 2005 #4
    if it was tossed the exact same way it would land on the same side every time. if the take a piece of plywood and intenenally try to drop it on a cretain side you probably would not get a 50/50
     
  6. Feb 7, 2005 #5
    Wouldn't such an accurate system make the coin fall either ONLY heads or only tails??? ---you know, same speed, spin, height...."same landing"--you mean only heads/tails?
     
  7. Feb 8, 2005 #6

    mathman

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    In theory, it might be possible to construct a device so that it always comes out heads. However, in practice there is usually enough jitter in the machinery so that it won't happen.
     
  8. Feb 8, 2005 #7

    DaveC426913

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    Gee, at first it seemd so paradoxical, but it isn't is it?

    Say the hypothetical perfect machine can overcome all physical variables, and throw the coin exactly the same way every time. My first thought was: "Oh, it would have to throw 5 and 5.".

    But no, it merely throws 10 of either heads or tails.

    You still don't have a machine that can throw exactly half-way in between. That requires manual tuning, and that's not perfect. And even if you could, you'd just end up with a machine that can balance coins on their edge every time.

    What you don't have, is a machine that helps you do probability experiments, since all the probability has been removed from the system.
     
    Last edited: Feb 8, 2005
  9. Feb 12, 2005 #8
    DaveC426913:What you don't have, is a machine that helps you do probability experiments, since all the probability has been removed from the system.

    That is why they use a "random number" system in computers, though how that is constructed is a matter all of its own.


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