math probability question for seven American nights

Gwern Branwen · 07 Sep 2014, 14:16 · from 2014-September.txt.gz

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From: gwern at gwern.net (Gwern Branwen)
Date: Sun, 7 Sep 2014 10:16:58 -0400
Subject: (urth) math probability question for seven American nights
In-Reply-To: <540C5B6C.8050407 at bindweed.com>
References: <CAF1072wp4W1u7KmwZpc=u4x7NtHz3136ZdKQbarnnVaKpxCw+w at mail.gmail.com>
	<540C5B6C.8050407 at bindweed.com>
Message-ID: <CAMwO0gxhO=PqEZAiPpYh0kvL+x0f+o+rkQD4m3QpAhorH32Ywg at mail.gmail.com>

On Sun, Sep 7, 2014 at 9:19 AM, Gerry Quinn <gerry at bindweed.com> wrote:
> I don't have the book to hand, but if he is given six eggs, one special, and
> eats one every day at random, the chance of getting the special egg on any
> day is indeed 1/6, as you reckoned in your other post.
>
> The easiest way to see it is to imagine he decided at random the order to
> eat them in advance, and laid all six in a row, each marked with its day for
> eating.  Clearly the chance is the same for each day!

Exactly. On the other hand, if he has some source of information about
the egg, then conditional on his new information each day, he may be
able to update his beliefs as he goes along and do better than
guessing just 1/6th each day.

As it happens, there's some literary precedent here: Graham Green's
novel https://en.wikipedia.org/wiki/Doctor_Fischer_of_Geneva_or_The_bomb_party

And if one doesn't know the egg is there, then it becomes an
interesting statistical problem:
http://gwern.net/docs/statistics/1994-falk

-- 
gwern

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