My sister was assigned a new 7-digit phone number that differs from mine only in the first and last digits.
probability/phone.numbers New
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Problem
My sister was assigned a new 7-digit phone number that differs from mine only in the first and last digits. How unlikely is such a coincidence? [ Editor: problem statement reconstructed from the posting by Naresh K Malhotra, which also discusses phone company rules for prefixes. ]
Show solution
In article <2pgkmf$ggn@vixen.cso.uiuc.edu>,
Naresh K Malhotra <whalen@news.cso.uiuc.edu.uucp> wrote:
>(1) The first digit of the prefix cannot be 0 or 1.
>(2) The second digit of the prefix cannot be 0 or 1.
While I believe that this was true historically, my current phone
number has a 1 as the second digit.
>Based on these assumptions, I calculated that the odds against two
>phone numbers being this similar were on the order of 100,000 to 1
>against. How accurate do you think this calculation is?
Not sure about your numbers (I didn't even check the math), but it
seems that the probability that you would really care about is that
the two numbers differ by only two (or even one or three) digits. Your
sister (and you) would still have noticed the similarity if it had been
other than the first and last digits.
Neglecting the above phone number choosing rules:
Probability that two random 7-digit numbers differ by exactly 2
digits:
(7 C 2) * 9 * 9 1701
--------------- = ------- = 1 in 5879
(10 ^ 7) - 1 9999999
Probability that two random 7-digit numbers differ by not more than 3
digits:
(7 C 1) * 9 + (7 C 2) * 9 * 9 + (7 C 3) * 9 * 9 *9
--------------------------------------------------
(10 ^ 7) - 1
27279
= ------- = 1 in 367
9999999
Not too improbable..... (and the above rules would lower it some more).
-- Ren Maddox <lhmaddox@bnr.ca>