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From: Russell Hendel <rhendel@saber.towson.edu>
Date: Sun, 9 Jul 2000 23:33:24 -0400 (EDT)
Subject: The MJ Answer to the "ending in 50" problem

Chaim Manaster enlarges upon my grandfathers question.

It seems to me that the same answer (that was given in MJ several years
ago) would apply to his enlarged question. Here is a brief summary

Assume the following rule: Round all Biblical numbers to the nearest 100
UNLESS the number ends in exactly 50. So eg 1234 1289 and 1250 would
appear as 1200 1300 and 1250 respectively

We can now ask the probability that among 16 tribes exactly 1 should
have an exact count of 50. This is a routine exercise in introductory
probability courses and is equal to 13.8%, not an unreasonable
number. (If we only deal with 12 tribes the probability of exactly one
census ending in 50 is 10.7%)

An intuitive defense of this number is as follows: The probability of a
census ending in 50 is 1% (since only 1 2-digit number ends in 50)
However there are 16 tribes which can have this census ending in 50.
Hence the probability that one of them ends in 50 is roughly 16%. We
however must multiply this 16% by the probability that NO OTHER tribe
ends in 50. There are 99 out of 100 ways that a tribe will not end in
50. Combining all the numbers we get 13.8%

Hope this helps

Russell Jay Hendel; Phd ASA; Math Towson; RHendel@Towson.edu
Moderator Rashi is Simple
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