math probability question for seven American nights

Gerry Quinn · 07 Sep 2014, 13:19 · from 2014-September.txt.gz

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From: gerry at bindweed.com (Gerry Quinn)
Date: Sun, 07 Sep 2014 14:19:40 +0100
Subject: (urth) math probability question for seven American nights
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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

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