A Ducal Coincidence

[Louis Epstein]

On May 15th,the 11th Duke of Atholl died at 83...the third Duke of Atholl
to die in the present reign,succeeded by his son,the first Duke of Atholl
born in the present reign.(The other two successions were cousin to
cousin).

Despite their being fewer Dukes than there are days in a month,
the late Duke shared his birthday (January 19th) with one other Duke
(St. Albans),and the new Duke shares his (April 6th) with two (Montrose
and Grafton).

Here's the full set of family titles:

Dukedom Marquessate Earldom Viscounty Barony


Atholl Atholl, Tullibardine, Balquhidder, Murray of
Tullibardine Atholl, Glenalmond Tullibardine,
Strathtay and and Glenlyon Murray Balvenie
Strathardle and Gask

The late Duke grew up in South Africa with his eventual succession
not remotely contemplated at the time.

-=-=-
The World Trade Center towers MUST rise again,
at least as tall as before...or terror has triumphed.

[David Uri]

On Sun, 20 May 2012 05:32:34 +0000 (UTC), Louis Epstein
<l...@main.put.com> wrote:

>Despite their being fewer Dukes than there are days in a month,
>the late Duke shared his birthday (January 19th) with one other Duke
>(St. Albans),and the new Duke shares his (April 6th) with two (Montrose
>and Grafton).

It's not really a coincidence at all. It only needs 23 people in a
group for the probability of at least two of them sharing a birthday
to be 50-50.

See, for example, http://en.wikipedia.org/wiki/Birthday_problem

Regards,
--
David Uri.
Please visit my town - http://allezblancs.miniville.fr
Every visitor increases the population by one.
Email: davidu...@bigfoot.com (remove VEST to reply)
Facebook: http://facebook.com/daviduri

[David]

On May 20, 5:56 am, David Uri <daviduriV...@bigfoot.com> wrote:
> On Sun, 20 May 2012 05:32:34 +0000 (UTC), Louis Epstein
>
> <l...@main.put.com> wrote:
> >Despite their being fewer Dukes than there are days in a month,
> >the late Duke shared his birthday (January 19th) with one other Duke
> >(St. Albans),and the new Duke shares his (April 6th) with two (Montrose
> >and Grafton).
>
> It's not really a coincidence at all.  It only needs 23 people in a
> group for the probability of at least two of them sharing a birthday
> to be 50-50.
>

> See, for example,http://en.wikipedia.org/wiki/Birthday_problem
>
> Regards,
> --
> David Uri.

Don't bother trying to explain it to Louis -- his mathematical
abilities top out at dividing by two.

[Louis Epstein]

In alt.obituaries David <ds...@softhome.net> wrote:

: On May 20, 5:56?am, David Uri <daviduriV...@bigfoot.com> wrote:
:> On Sun, 20 May 2012 05:32:34 +0000 (UTC), Louis Epstein
:>
:> <l...@main.put.com> wrote:
:> >Despite their being fewer Dukes than there are days in a month,
:> >the late Duke shared his birthday (January 19th) with one other Duke
:> >(St. Albans),and the new Duke shares his (April 6th) with two (Montrose
:> >and Grafton).
:>

:> It's not really a coincidence at all. ?It only needs 23 people in a

:> group for the probability of at least two of them sharing a birthday
:> to be 50-50.
:>
:> See, for example,http://en.wikipedia.org/wiki/Birthday_problem

:>
:
: Don't bother trying to explain it to Louis -- his mathematical

: abilities top out at dividing by two.

http://www.put.com/A/bignumb.html

Quite a bit higher than two!

[Louis Epstein]

In alt.obituaries David Uri <davidu...@bigfoot.com> wrote:
: On Sun, 20 May 2012 05:32:34 +0000 (UTC), Louis Epstein

: <l...@main.put.com> wrote:
:
:>Despite their being fewer Dukes than there are days in a month,
:>the late Duke shared his birthday (January 19th) with one other Duke
:>(St. Albans),and the new Duke shares his (April 6th) with two (Montrose
:>and Grafton).
:
: It's not really a coincidence at all. It only needs 23 people in a
: group for the probability of at least two of them sharing a birthday
: to be 50-50.

Yet this is the statistical universe in question:


Jan 19 1939 St. Albans D
Feb 14 1954 Buccleuch & Queensberry D
Feb 18 1940 Sutherland D
Feb 23 1928 Beaufort D
March 30 1962 Bedford D
March 31 1978 Hamilton & Brandon D
April 6 1935 Montrose D
April 6 1960 Atholl D
April 6 1978 Grafton D
April 7 1948 Leinster D
April 13 1926 Marlborough D
May 8 1959 Rutland D
May 29 1968 Argyll D
July 2 1915 Wellington D
July 4 1934 Abercorn D
Sept 19 1929 Richmond & Lennox & Gordon D
Sept 23 1929 Fife D
Nov 16 1956 Northumberland D
Nov 18 1954 Roxburghe D
Dec 2 1956 Norfolk D
Dec 11 1962 Manchester D
Dec 22 1951 Westminster D
Dec 30 1952 Somerset D

It contained TWO pairs and now contains a trio...more remarkable than a
single pair!

[The Chief]

And what is the probability that you are addicted to meaningless
numerology?

Regards,
The Chief

[J.D. Baldwin]

In the previous article, David Uri <davidu...@bigfoot.com> wrote:
> >Despite their being fewer Dukes than there are days in a month,
> >the late Duke shared his birthday (January 19th) with one other Duke
> >(St. Albans),and the new Duke shares his (April 6th) with two (Montrose
> >and Grafton).
>
> It's not really a coincidence at all. It only needs 23 people in a
> group for the probability of at least two of them sharing a birthday
> to be 50-50.

First off, that doesn't make it not a coincidence. It's just not a
very unusual coincidence.

So, given 23 individuals, the probability that some two of them will
share a birthday is about 0.51.

The probability that, of the remaining 21 individuals, *three* of them
will share a different birthday, is about 0.025.

The probability that, in a group of 23 people, two will share one
birthday and three will share another (without regard to other
possible such coincidences in the same set) is the product of these
two values, or about 0.013 -- a little better than one in eighty.

(Leap years and natural birth "clustering" ignored for calculation
purposes. Their real-world effects are probably out in the sixth or
seventh significant digit and I have confined myself to two.)

I consider 1-in-80 to be at least kind of a noteworthy coincidence.
--
_+_ From the catapult of |If anyone objects to any statement I make, I am
_|70|___:)=}- J.D. Baldwin |quite prepared not only to retract it, but also
\ / bal...@panix.com|to deny under oath that I ever made it.-T. Lehrer
***~~~~----------------------------------------------------------------------

[David Uri]

On Mon, 21 May 2012 16:49:26 +0000 (UTC),
INVALID...@example.com.invalid (J.D. Baldwin) wrote:
>
>In the previous article, David Uri <davidu...@bigfoot.com> wrote:
>> >Despite their being fewer Dukes than there are days in a month,
>> >the late Duke shared his birthday (January 19th) with one other Duke
>> >(St. Albans),and the new Duke shares his (April 6th) with two (Montrose
>> >and Grafton).
>>
>> It's not really a coincidence at all. It only needs 23 people in a
>> group for the probability of at least two of them sharing a birthday
>> to be 50-50.
>
>First off, that doesn't make it not a coincidence. It's just not a
>very unusual coincidence.
>
>So, given 23 individuals, the probability that some two of them will
>share a birthday is about 0.51.
>
>The probability that, of the remaining 21 individuals, *three* of them
>will share a different birthday, is about 0.025.
>
>The probability that, in a group of 23 people, two will share one
>birthday and three will share another (without regard to other
>possible such coincidences in the same set) is the product of these
>two values, or about 0.013 -- a little better than one in eighty.
>
>(Leap years and natural birth "clustering" ignored for calculation
>purposes. Their real-world effects are probably out in the sixth or
>seventh significant digit and I have confined myself to two.)
>
>I consider 1-in-80 to be at least kind of a noteworthy coincidence.

Thanks for doing the maths - it's a long time since I did probability
theory. Yes, I agree that the combination of a pair and a triple is
unusual.

Incidentally, one other obvious requirement for the calculations to be
valid is that the group doesn't contain any sets of twins, triplets,
etc.

I hesitate to ask Louis whether there would be any more coincidences
if the Royal Dukes were included?

[Louis Epstein]

In alt.obituaries David Uri <davidu...@bigfoot.com> wrote:

: On Mon, 21 May 2012 16:49:26 +0000 (UTC),

There actually weren't a combination of a pair and a triple,
but a single death simultaneously dissolved a pair and created
a triple.Not sure how to calculate the odds for that!

: Incidentally, one other obvious requirement for the calculations to be

: valid is that the group doesn't contain any sets of twins, triplets,
: etc.

Only one of a set could inherit a title at a time.

: I hesitate to ask Louis whether there would be any more coincidences

: if the Royal Dukes were included?

There would not.