Which day of the week (Sunday, Monday, etc.) is the probability largest to fall on the 13th of a random month, in a random year?
Or is this probability the same for each day of the week?
(In reply to
re: solution and discussion by Elisabeth)
"But this means that, if you have considered the interval 20012400, your counting would have been different, and yet other values would arise if you took the 20102309 period. So, 400 years are not a significant sample."
Of course the 20102309 period would result in different numbers: that is only a 300year period, while the Gregorian calendar has a 400year cycle. However any 400 successive years will have the same distribution of dates vs days of the week in the Gregorian calendar. Thus if the period were 20102409, it would have the same distribution as 20012400. The calendar for 2401 is exactly the same as for 2001, beginning on a Monday and 365 days long, and 2402 has the same calendar as 2002, all the way through to 2409 being the same as 2009. So swapping those sets of 9 years has no net change.
So the distribution from 20012400, significantly for counting purposes, is the same as for 24012800, and for 28013200, etc., the reason again being that (1) the leap year pattern is the same and (2) each of these 400year periods begins on a Monday. And the coincidence of Mondays (that is, a particular day of the week, that by our boundary choice is Monday) results from the number of days in 400 years being an exact multiple of seven (365.25 x 400  3 = 146097 = 20871 x 7 exactly).
By the way, I took 20002399, but that's the same as 20012400 because 2000 had the same calendar as 2400 will have. The 400 year cycle I chose began on a Saturday, Jan. 1,2000, and Jan 1, 2400 will begin on a Saturday also.
Edited on August 30, 2004, 8:25 pm

Posted by Charlie
on 20040830 20:19:42 