Re: Eliezer's Coin Flipping Duplicates Paradox

From: William Pearson (wil.pearson@gmail.com)
Date: Mon Mar 10 2008 - 10:22:48 MDT

On 10/03/2008, Lee Corbin <lcorbin@rawbw.com> wrote:
> 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?
> >>
> >> Sorry, I don't follow your reasoning and arithmetic. Can you
> >> 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.
>

My point was that 90% of the time in this experiment everyone dies, so
0 people should be the expectation after 5 rounds. You calculated the
expectation after one round and extrapolated, which I think was wrong.

I did the math for the probability of exactly one person surviving*
and it is 37 % chance, the same as the chance that everyone dies.
However the chance of exactly one person surviving has to be less than
10% after 5 rounds.

Will Pearson

* 1/101*((100/101)^100)*101 = 0.37

This archive was generated by hypermail 2.1.5 : Wed Jul 17 2013 - 04:01:02 MDT