# Friday The 13Th

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Friday the 13th came on Friday this month (as Pogo would say). Is the probability of that happening exactly one seventh, or is it more complicated than that for some reason?
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Friday the 13th came on Friday this month (as Pogo would say). Is the probability of that happening exactly one seventh, or is it more complicated than that for some reason? Comments?

The probability of Friday the 13th being on a friday is 100%.
Friday the 13th came on Friday this month (as Pogo would say). Is the probability of that happening exactly one seventh, or is it more complicated than that for some reason?

It is more complicated than that because different months have different numbers of days. You will find Friday the 13th occurs twice in some years and at other frequencies in other years, varying according to the day of Jan. 1. The arithmetic is laborious but simple, so you can do it yourself.

Don Phillipson
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Friday the 13th came on Friday this month (as Pogo would say).

Actually, it was Churchy (Cherchez LaFemme) who was obessesed with Friday the 13th, irrespective of what day it actually fell on.
Is the probability of that happening exactly one seventh, or is it more complicated than that for some reason? Comments?

The probability of Friday the 13th being on a friday is 100%.

Not if you are Churchy! And I suspect the the OP meant what are the odds of the 13th of any month falling on Friday. As for that, I don't know. There are 14 basic yearly calanders (one set of 7 for regular years, and one for Leap Years).
Barbara Need
UChicago Linugistics
Friday the 13th came on Friday this month (as Pogo would say). Is the probability of that happening exactly one seventh, or is it more complicated than that for some reason? Comments?

Strictly speaking, the probability of Friday the 13th falling on a Friday is 1.0, but to say in Pogo-talk "Friday the 13th came on a Friday" means the same as most people saying "The 13th fell on a Friday."
I don't know what the probability is that the 13th will fall on a Friday, but the number of "Friday the 13th"s in each of
11 years is (if I counted right):
2000 1
2001 2
2002 2
2003 1
2004 2
2005 1
2006 2
2007 2
2008 1
2009 3
2010 2

That's 19 times in 132 months.
19/132=~0.1439. 1/7 would be 19/133=~0.1429. That doesn't prove anything, of course, except to the easily convinced.
Friday the 13th came on Friday this month (as Pogo ... or is it more complicated than that for some reason?

The probability of Friday the 13th being on a friday is 100%.

Brian Rodenborn
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Raymond O'Hara:
The probability of Friday the 13th being on a friday is 100%.

Barbara Need:
... I suspect the the OP meant what are the odds of the 13th of any month falling on Friday.

If the number of days in one cycle of the leap-year pattern under the Gregorian calendar wasn't a multiple of 7, then the probability would necessarily be exactly 1/7, but it is (97 leap years + 303 common years = 146,097 days = 20,871 weeks exactly), so it isn't. Over the 4,800 months in the cycle, a simple brute-force check (using "cal" on UNIX) shows that the 13th falls:
687 times on Sunday
685 times on Monday
685 times on Tuesday
687 times on Wednesday
684 times on Thursday
688 times on Friday
684 times on Saturday

So the probability is 688/4800 = 43/300, or just slightly greater than 1/7 = 43/301.

"But even though they probably certainly know that you probably wouldn't, they don't certainly know that although you probably wouldn't there's no probability that you certainly would." Sir Humphrey Appleby ("Yes, Prime Minister") on nuclear deterrence

Friday the 13th came on Friday this month (as Pogo would say). Is the probability of that happening exactly one seventh, or is it more complicated than that for some reason?

The modern calendar repeats every 400 years. In that time there are exactly
12 x 400 = 4800 months, each with one 13th day. If you count all of themthat land on a Friday, you should get 688. That sets the probability of Friday the 13th at 688 out of 4800, which reduces to 43 out of 300, or about .1433. One in seven would be about .1429, so the actual probability is a little greater than 1:7.
Don
Kansas City
Actually, it was Churchy (Cherchez LaFemme) who was obessesed with Friday the 13th, irrespective of what day it actually fell on.

Nobody seems to remember that but you and me. Every once in a while I used to make a remark like, "Friday the 13th comes on a Tuesday this month," and all I would get back were blank stares so I stopped doing it.

John Varela
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