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Math Help - 13th of a month

  1. #1
    Super Member malaygoel's Avatar
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    13th of a month

    Show that the 13th of a month falls more frequently on Friday than on any other day.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by malaygoel
    Show that the 13th of a month falls more frequently on Friday than on any other day.
    See Here
    (the calendar has a 400 year cycle, and the frequencies need to be computed
    over such a cycle - the intuitive equiprobability model for date/day distribution
    is broken up by the leap/non-leap rules for years divisible by 100).

    RonL
    Last edited by CaptainBlack; June 5th 2006 at 12:09 AM.
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  3. #3
    Super Member malaygoel's Avatar
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    Quote Originally Posted by CaptainBlack
    See Here
    (the calendar has a 400 year cycle, and the frequencies need to be computed
    over such a cycle - the intuitive equiprobability model for date/day distribution
    is broken up by the leap/non-leap rules for years divisible by 100).

    RonL
    What is special about 13 and friday? Can't the same question be asked by replacing 13 by 12 and/or friday by any other day?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by malaygoel
    What is special about 13 and friday? Can't the same question be asked by replacing 13 by 12 and/or friday by any other day?
    The combination of day & date have slightly different frequencies - it just so
    happens that for the 13th of the month the day with maximum frequency
    is Friday.

    RonL
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  5. #5
    Super Member malaygoel's Avatar
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    Quote Originally Posted by CaptainBlack
    The combination of day & date have slightly different frequencies - it just so
    happens that for the 13th of the month the day with maximum frequency
    is Friday.

    RonL
    Does it mean that it is just a coincidence?
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by malaygoel
    Does it mean that it is just a coincidence?
    Depends on why you think Friday the 13th is or is not significant.

    Its a property of the Gregorian Calendar, IIRC doesn't happen in the Julian
    Calendar.

    RonL
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  7. #7
    Super Member malaygoel's Avatar
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    Quote Originally Posted by CaptainBlack
    Depends on why you think Friday the 13th is or is not significant.

    Its a property of the Gregorian Calendar, IIRC doesn't happen in the Julian
    Calendar.

    RonL
    I have a doubt. Let January1 of 2001 falls on monday(I don't know exactly).
    Then in the cycle of 400 years 13th of a month falls frequently on fridays.
    If it would have been tuesday instead of monday, then 13th of a month would have fallen on saturdays(right????).
    So it is just of trivial importance that we have January1 on such a day that 13th of a month falls on fridays. It has nothing to do with the probability. It is a fact that friday and 13 are good friends due to the day we assigned to January1 of 2001.
    I hope you understand what I want to say.
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  8. #8
    Grand Panjandrum
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    Quote Originally Posted by malaygoel
    I have a doubt. Let January1 of 2001 falls on monday(I don't know exactly).
    Then in the cycle of 400 years 13th of a month falls frequently on fridays.
    If it would have been tuesday instead of monday, then 13th of a month would have fallen on saturdays(right????).
    So it is just of trivial importance that we have January1 on such a day that 13th of a month falls on fridays. It has nothing to do with the probability. It is a fact that friday and 13 are good friends due to the day we assigned to January1 of 2001.
    I hope you understand what I want to say.
    Yes I understand, and yes a shift of 1 day in the phase of the calendar
    would result in a different day having the greatest frequency of being
    the 13th of the month.

    RonL
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  9. #9
    Super Member malaygoel's Avatar
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    Quote Originally Posted by CaptainBlack
    Yes I understand, and yes a shift of 1 day in the phase of the calendar
    would result in a different day having the greatest frequency of being
    the 13th of the month.

    RonL
    Thanks for your help.
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