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© Copyright 1999, Jim Loy
Friday the 13th is, of course, considered unlucky by some people. Personally, it is one of that many delightful holidays (including all Mondays) that I take off from work. I also joke that I can prove that no month has more than one Friday the 13th.
Examining a perpetual calendar (in the World Almanac) I see that we have a Friday the 13th whenever the month begins on a Sunday. I also see that every year has at least one and at most three Friday the 13ths (usually there are two). 1998 had three, 1999 had one, 2000 will have one. There can also be Friday the 13th in two consecutive months (February and March) as there were in 1998.
The probability that any randomly selected month will have a Friday the 13th would seem to be 1/7 (.1428571428...), as there are only seven types of month (ones that begin on Sunday, Monday, ...). And each would seem to be equally likely. It turns out that this is not quite true. It was shown by Brown (I don't know his first name) in 1933 that the Gregorian Calendar (which we use) repeats itself exactly, every 400 years. In that time, there are 4800 months and 4800 13ths. Of those 4800 13ths, 688 occur on Friday. So the probability of a Friday the 13th is 688/4800 which is .143333..., which is slightly greater than 1/7. In fact, Friday is the most likely 13th, slightly. Of the 4800 13ths, Sunday is the 13th 687 times, Mondya 685, Tuesday 685, Wednesday 687, Thursday 684, Friday 688, and Saturday 684.
A couple of years ago, I was about to report (on these WWW pages) that the probability of a Friday the 13th was 1/7. But I never got around to it.