# Re: Eliezer's Coin Flipping Duplicates Paradox

From: William Pearson (wil.pearson@gmail.com)
Date: Sun Mar 09 2008 - 04:43:12 MDT

On 09/03/2008, Lee Corbin <lcorbin@rawbw.com> wrote:
>
>
> Consider the case now after five days have passed. We compute
> that the expectation is that just one of you will still be
> alive, because every day 100/101 are eliminated, whether or
> not they saw an H or a T.
>
>
> What will this one remember? It's possible that he will remember
> TTTTT, but that is very unlikely. That would only occur if each
> day the 100/101 death toll struck only those who had received
> "heads". The chances are (100/101)^5, which is close to .95,
> that he would remember HHHHH.
>
> And if this continues, then a "T" will crop up in a long sequence
> of mostly H's about one time in one hundred and one.
>
> Therefore, as before, the subjective probability is 100/101
> that on each trial you'll see an H.
>
>
> William writes
>
>
> > Isn't there only a 64% chance anyone will be alive after one
> > iteration? And after 5 iterations only a 10.2% chance that
> > anyone will be alive?
>
>
> explain?
>

Chance one person will die 100/101
Chance that everyone will die on one day (100/101)^101 = 0.366
So the chance that at least one person will survive a single day =
1-.366 = 0.634
So the chance that at least one person will be alive after 5 days =
0.634^5 = 0.102

Am I going wrong somewhere?

Will Pearson

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