math probability question for seven American nights - CORRECTION

Gerry Quinn · 07 Sep 2014, 13:26 · from 2014-September.txt.gz

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From: gerry at bindweed.com (Gerry Quinn)
Date: Sun, 07 Sep 2014 14:26:41 +0100
Subject: (urth) math probability question for seven American nights -
 CORRECTION
In-Reply-To: <540C5B6C.8050407 at bindweed.com>
References: <CAF1072wp4W1u7KmwZpc=u4x7NtHz3136ZdKQbarnnVaKpxCw+w at mail.gmail.com>
	<540C5B6C.8050407 at bindweed.com>
Message-ID: <540C5D11.5080106 at bindweed.com>

On 07/09/2014 14:19, Gerry Quinn wrote:
>
> On 07/09/2014 13:34, Marc Aramini wrote:
>> I had a quick question but trying to articulate it to look it up 
>> independently is hard.
>>
>> Is there a statistically most probable day for Nadan to eat the 
>> special one of the six eggs on any given day given that the first day 
>> is 1/6 and then from there the probability that the egg is there 
>> begins to be something like 1/5  on the next day ( but the chance 
>> that it isn't there should be factored in somehow, but I wasn't sure 
>> if it was 1/5 - 1/6 ... Then 1/4-1/5-1/6 etc. ) Or is the system set 
>> up in such a way that the chance of getting the egg is always 1/6 
>> regardless on any given morning assuming no eggs are stolen or 
>> disappear?
>>
>
> 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!
>
> - Gerry Quinn

Actually, that is the chance before the experiment,  If the first egg is 
to be eaten on Sunday, then before he eats it he knows that the chance 
of eating the special egg on any given day (say Tuesday) is 1/6.

But that presupposes he has no clue as to when he has eaten the special 
egg.  If he can tell immediately, then after he eats Sunday's egg. he 
knows that either it was the special one, or it wasn't.  Depending on 
which, the chance that he will eat the special egg on Tuesday becomes 
either zero, or 1/5.

If he has some information that might help him decide which egg is 
special, but cannot be certain, the answer is somewhere in between. I 
cannot remember the story well, but I suspect this is most likely the 
situation!

- Gerry Quinn

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