[Bell Historians] 'Bell weights' A mathematician responds

[Peter Humphreys]

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I am not a mathematician but I suspect the probabilities being quoted
are for any specified ring. If there were 500 million rings of six bells
then the probability would, I guess, be unity of one ring having all
bell weights ending in 0.

But the number of rings is only in the thousands so the probability must
be low. However, ANY combination of lbs has an equal chance of occurring
as any other, so one tower having all ending is zero is possible,
however seemingly unlikely. The same is true for numbers 1 to 7 being
the winning numbers in the National Lottery. I understand statistics
sufficiently not to waste my money on that! (Some just think I am rather
too careful with my money i.e. mean!)

However, it is prudent to suspect a high incidence of bell weights
ending in zero, especially if, over a large enough sample, this is
higher than about 1 in 28. Has anyone out there done such an analysis?

-----Original Message-----
From: Andrew Aspland [mailto:aaspland at y...] 
Sent: 28 September 2004 17:12
To: bellhistorians at yahoogroups.com
Subject: [Bell Historians] 'Bell weights' A mathematician responds


Glad we have cleared up the "quarter of a quarter" problem. Assuming
that bell weights randomly end in any number of pounds from 0 to 27 then
there is a 4/28 = 1/7 probability that the weight will end in 0,7,14 or
28. This is a reasonable assumption given teh range of weights we are
considering but would not be true for very small bells. 

For a ring of six to all end in such a number the probability would be
1/7^6 which is 0.000008499 in other words less than a 1 in 100 000
chance - be VERY suspisious. Even for a ring of four this is less than
a 1 in 2000 chance.

For all six bells to end in 0 (Shaftsbury) the probability would be
1/28^6 which is 0.000000002 or around a 1 in 500 000 000 chance.
Statistically I do not believe that Shaftsbury all ended in 0.

For any two bells out of eight to end in 0 is a less than 4% chance -
worth checking!

Andrew

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