Thread: 13th of a month

Show that the 13th of a month falls more frequently on Friday than on any other day.

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

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?

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

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?

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

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.

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

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.