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Thread: Probability

  1. #1 Probability 
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    Hi,
    If three coins are tossed simultaneously, the following are possible:
    {HHH, HHT, HTH, TTH, TTT, THH, THT, HTT}
    In this case n(S) = 8.
    It can be written in smaller cases.
    If I say, 10 coins are tossed simultaneously, how do I calculate the number of possibilities? Is there a formula to do the same?

    Thanks
    Ashwin


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  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Each new coin doubles the number of possibilities, so it's just 2^n.


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  4. #3  
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    Well, that seems to work in the case of coins. What if two dice are thrown, then there are 36 possibilities.
    So is there a general formula for all of these cases?
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  5. #4  
    Genius Duck Moderator Dywyddyr's Avatar
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    Two dice = 62 possible results.
    Three dice = 63.
    Same rule.
    Number of possible results of one [coin/ die]number tossed/ rolled.
    "[Dywyddyr] makes a grumpy bastard like me seem like a happy go lucky scamp" - PhDemon
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  6. #5  
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    Ya well, there is a slight problem here (in mathematical terms)

    Suppose it is true that tossing coins, each with 2 possible outcomes gives a total of possible outcomes.

    Now suppose I toss zero coins just once - don.t say this is not "physically possible", in mathematics this is irrelevant. So zero coins tossed just once has possible outcomes. Can this be true?

    Does it help to note that tossing coins just once has exactly the same number of possible outcomes as tossing a single coin times? Well, tossing a single coin zero times reveals the starting face, that is only outcomes.

    What gives? Your homework is to provide a mathematical answer
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  7. #6  
    Genius Duck Moderator Dywyddyr's Avatar
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    Quote Originally Posted by Guitarist View Post
    Now suppose I toss zero coins just once - don.t say this is not "physically possible", in mathematics this is irrelevant. So zero coins tossed just once has possible outcomes. Can this be true?
    I just spent fifteen minutes tossing zero coins.
    And always got the same result.
    That's close enough for me.
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  8. #7  
    Bullshit Intolerant PhDemon's Avatar
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    ^^ Spot the engineer
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  9. #8  
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    Well I just tossed –1 coins and only got half an outcome.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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  10. #9  
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    Quote Originally Posted by Guitarist View Post
    Ya well, there is a slight problem here (in mathematical terms)

    Suppose it is true that tossing coins, each with 2 possible outcomes gives a total of possible outcomes.

    Now suppose I toss zero coins just once - don.t say this is not "physically possible", in mathematics this is irrelevant. So zero coins tossed just once has possible outcomes. Can this be true?

    Does it help to note that tossing coins just once has exactly the same number of possible outcomes as tossing a single coin times? Well, tossing a single coin zero times reveals the starting face, that is only outcomes.

    What gives? Your homework is to provide a mathematical answer
    How can you be sure you tossed the zero coins only once?
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  11. #10  
    Forum Junior anticorncob28's Avatar
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    So zero coins tossed just once has 2^0 = 1 possible outcomes. Can this be true?
    Yes. If there were zero outcomes of tossing zero coins, that would make it impossible to not flip zero coins. It would mean that no matter where you are or what you're doing, you would have to be flipping at least one coin.
    UNIVERSAL TRUTHS:
    1) There are no universal truths, other than this one.
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  12. #11  
    Forum Junior TridentBlue's Avatar
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    You also say "It can be written in smaller cases." Do you mean where you count HTT, THT, TTH (two tails one head) and as one outcome? If you want the formula with probability for that, you need the binomial distribution:

    https://en.wikipedia.org/wiki/Binomial_distribution

    If you toss 10 coins simultaneously, it will give the probability of each outcome (3 heads, 4 heads, etc)
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  13. #12  
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    Quote Originally Posted by Guitarist View Post
    Ya well, there is a slight problem here (in mathematical terms)

    Suppose it is true that tossing coins, each with 2 possible outcomes gives a total of possible outcomes.

    Now suppose I toss zero coins just once - don.t say this is not "physically possible", in mathematics this is irrelevant. So zero coins tossed just once has possible outcomes. Can this be true?

    Does it help to note that tossing coins just once has exactly the same number of possible outcomes as tossing a single coin times? Well, tossing a single coin zero times reveals the starting face, that is only outcomes.

    What gives? Your homework is to provide a mathematical answer
    The simple answer is you are not talking a probability because…


    Probable outcome is given (desired outcome / possible outcomes). You have no desired outcome only a possible outcome.
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  14. #13  
    Genius Duck Moderator Dywyddyr's Avatar
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    Quote Originally Posted by GTCethos View Post
    The simple answer is you are not talking a probability because…
    Probable outcome is given (desired outcome / possible outcomes). You have no desired outcome only a possible outcome.
    Arrant nonsense.
    Probability has nothing whatsoever to do with "desired outcome".
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