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Math Help - Longest run in 50 tosses

  1. #1
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    Question Longest run in 50 tosses

    Hello....

    How do I find the longest run in fifty tosses of a coin?
    To add to this question, how do I compare two sequences of coin tosses to differentiate between real toss and the fake toss?
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  2. #2
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    Re: Longest run in 50 tosses

    Longest run of what? Is the coin fair? What exactly is a "fake toss"?
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    Re: Longest run in 50 tosses

    the coin is fair. A fake toss is what I predict the sample space can be like.
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    Re: Longest run in 50 tosses

    Longest run of Heads, I mean...
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    Re: Longest run in 50 tosses

    Quote Originally Posted by hsetima View Post
    Longest run of Heads, I mean...
    The longest possible run of heads in 50 tosses of a fair coin is ..... 50 heads. (Unlikely, yes. But impossible, no.)
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    Re: Longest run in 50 tosses

    It may be possible. But is there any way of calculating it - maybe by relative frequencies based on an experiment?
    But I managed to find a formula - log of n in base 2. In my case it gave me the longest run to be 5.6 - it can be either be of heads or tails, but I cant explain how.....
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  7. #7
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    Re: Longest run in 50 tosses

    Quote Originally Posted by hsetima View Post
    It may be possible. But is there any way of calculating it - maybe by relative frequencies based on an experiment?
    \text{(longest possible run of heads)}=\text{(total of times that you flip the coin)}

    The possibility that you will flip a heads every single time always exists. If you flip a coin one million times in a row, then the longest possible run of heads is one million (extreeemely unlikely, but possible nevertheless).
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    Re: Longest run in 50 tosses

    Quote Originally Posted by hsetima View Post
    It may be possible. But is there any way of calculating it - maybe by relative frequencies based on an experiment?
    But I managed to find a formula - log of n in base 2. In my case it gave me the longest run to be 5.6 - it can be either be of heads or tails, but I cant explain how.....
    The longest possible run is 50 heads. The probability of it occuring is (1/2)^50.

    But I think what you want and what you asked are two different things. Perhaps you want the longest expected run ....
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    Re: Longest run in 50 tosses

    Yes Mr. Fantastic,
    I want the longest expected run
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  10. #10
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    Re: Longest run in 50 tosses

    Quote Originally Posted by hsetima View Post
    Hello....

    How do I find the longest run in fifty tosses of a coin?
    To add to this question, how do I compare two sequences of coin tosses to differentiate between real toss and the fake toss?
    Post the real problem please.

    If this is a homework problem or from a book post it exactly as worded.

    If this is a practical problem post the context and what you are trying to do.

    CB
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