# Re: Eliezer's Coin Flipping Duplicates Paradox

From: Lee Corbin (lcorbin@rawbw.com)
Date: Sun Mar 09 2008 - 19:19:49 MDT

William writes

> [Lee 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
>> >> abecause 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

Ah, I was computing the expectation, i.e., the expected number of
instances alive. You are computing the chance that at least one
instance of the person will be alive.

Lee

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