Archiver > GENEALOGY-DNA > 2006-02 > 1139870014

From: (John Chandler)
Subject: Re: [DNA] Earliest common ancestors for 37/37 and 43/43 matches
Date: Mon, 13 Feb 2006 17:33:34 -0500 (EST)
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Diana wrote:
> The probability that two people in a group of 367 have
> the same birthdate is 1/367 times 1/367 or 1 in 134,689 thousand.

Not at all. Leaving aside the question of whether 365 or 366 is the
best number to use, what you're proposing has nothing to do with the
size of the group. The odds you're quoting are for the situation of
picking out two specific people at random and asking if they both have
the same birthday as YOU. That has nothing to do with the birthday
"paradox", which calls for asking everybody in a randomly chosen group
and finding out if at least two of them have the same birthday as each
other, not specifying WHICH two people in advance. Any two will do,
and any birthday will do. Essentially, you've demonstrated why this
thing is called a "paradox".

> In the case of STR testing for 37 markers, where 74 one-step mutations are
> possible from a common origin, the chance of two individuals having the same
> mutation is 1/74 times 1/74 or 1/5476.

Again, no. You've stated a number that is independent of the size of
the group, and therefore does not take into account any part of the
birthday paradox. The number you quote is the chance of picking out a
specific mutation in advance and then discovering that two specified
people (known somehow to have exactly one mutation each) BOTH have
that exact mutation. That's not relevant.

John Chandler

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