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<DIV><SPAN class=3D642500414-29092004><FONT face=3DArial color=3D#0000ff si=
ze=3D2>I am=20
not a mathematician but I suspect the probabilities being quoted are for an=
y=20
specified ring. If there were 500 million rings of six bells then the=20
probability would, I guess, be unity of one ring having all bell weights en=
ding=20
in 0.</FONT></SPAN></DIV>
<DIV><SPAN class=3D642500414-29092004><FONT face=3DArial color=3D#0000ff=20
size=3D2></FONT></SPAN> </DIV>
<DIV><SPAN class=3D642500414-29092004><FONT face=3DArial color=3D#0000ff si=
ze=3D2>But=20
the number of rings is only in the thousands so the probability must b=
e=20
low. However, ANY combination of lbs has an equal chance of occurring =
as=20
any other, so one tower having all ending is zero is possible, however seem=
ingly=20
unlikely. The same is true for numbers 1 to 7 being the winning numbers in =
the=20
National Lottery. I understand statistics sufficiently not to waste my mone=
y on=20
that! (Some just think I am rather too careful with my money i.e.=20
mean!)</FONT></SPAN></DIV>
<DIV><SPAN class=3D642500414-29092004><FONT face=3DArial color=3D#0000ff=20
size=3D2></FONT></SPAN> </DIV>
<DIV><SPAN class=3D642500414-29092004><FONT face=3DArial color=3D#0000ff=20
size=3D2>However, it is prudent to suspect a high incidence of bell weights=
ending=20
in zero, especially if, over a large enough sample, this is higher than abo=
ut 1=20
in 28. Has anyone out there done such an analysis?</FONT></SPAN></DIV>
<BLOCKQUOTE=20
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<DIV></DIV>
<DIV class=3DOutlookMessageHeader lang=3Den-us dir=3Dltr align=3Dleft><FO=
NT=20
face=3DTahoma size=3D2>-----Original Message-----<BR><B>From:</B> Andrew =
Aspland=20
[mailto:aaspland@y...] <BR><B>Sent:</B> 28 September 2004=20
17:12<BR><B>To:</B> bellhistorians@yahoogroups.com<BR><B>Subject:</B> [Be=
ll=20
Historians] 'Bell weights' A mathematician responds<BR><BR></FONT></DIV>
<DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN class=3D214055615-=
28092004>Glad=20
we have cleared up the "quarter of a quarter" problem. Assuming tha=
t=20
bell weights randomly end in any number of pounds from 0 to 27 then there=
is a=20
4/28 =3D 1/7 probability that the weight will end in 0,7,14 or 28. =
This is=20
a reasonable assumption given teh range of weights we are considering but=
=20
would not be true for very small bells. </SPAN></FONT></DIV>
<DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN=20
class=3D214055615-28092004></SPAN></FONT> </DIV>
<DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN class=3D214055615-=
28092004>For=20
a ring of six to all end in such a number the probability would be 1/7^6 =
which=20
is 0.000008499 in other words less than a 1 in 100 000 chance - be VERY=20
suspisious. Even for a ring of four this is less than a 1 in 2000=20
chance.</SPAN></FONT></DIV>
<DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN=20
class=3D214055615-28092004></SPAN></FONT> </DIV>
<DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN class=3D214055615-=
28092004>For=20
all six bells to end in 0 (Shaftsbury) the probability would be 1/28^6 wh=
ich=20
is 0.000000002 or around a 1 in 500 000 000 chance. Statistically I=
do=20
not believe that Shaftsbury all ended in 0.</SPAN></FONT></DIV>
<DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN=20
class=3D214055615-28092004></SPAN></FONT> </DIV>
<DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN class=3D214055615-=
28092004>For=20
any two bells out of eight to end in 0 is a less than 4% chance - worth=20
checking!</SPAN></FONT></DIV>
<DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN=20
class=3D214055615-28092004></SPAN></FONT> </DIV>
<DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN=20
class=3D214055615-28092004>Andrew</SPAN></FONT></DIV><!-- |**|end egp htm=
l banner|**| --><BR><BR><PRE>
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