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Archiver > GENEALOGY-DNA > 2010-11 > 1290275362


From: Steven Bird <>
Subject: Re: [DNA] Odds Are, It's Wrong - 5% of the time
Date: Sat, 20 Nov 2010 11:49:22 -0600
References: <F9C440A2-FC59-4A9E-AAAC-85DEE9D2FAB0@GMAIL.COM>, ,,,<COL115-W50D879F102DC3996D9D454A03A0@phx.gbl>,,,<COL118-W33D30F8531A4233CE0ED4EA03A0@phx.gbl>,, , <COL115-W265440F6CAC26EACE7E766A03B0@phx.gbl>, ,<COL115-W23D43856114A4E81F80053A03B0@phx.gbl>, ,<4CE7417F.7010909@san.rr.com>,<COL115-W160024221564BAFED8454CA03B0@phx.gbl>,<4CE7DBAE.3090408@san.rr.com>
In-Reply-To: <4CE7DBAE.3090408@san.rr.com>


Quoting the article:



############## begin quotation########################



We can see from the above that, if one flips a fair coin 21 times, then the probability of 21 heads is 1 in 2,097,152. However, the probability of flipping a head after having already flipped 20 heads in a row is simply 1⁄2. This is an application of Bayes' theorem.

This can also be seen without knowing that 20 heads have occurred for certain (without applying of Bayes' theorem). Consider the following two probabilities, assuming a fair coin:




probability of 20 heads, then 1 tail = 0.520 × 0.5 = 0.521
probability of 20 heads, then 1 head = 0.520 × 0.5 = 0.521


#################### end quotation####################


This is exactly what I thought I was saying. If I appeared to say otherwise, I apologize for being unclear. What I tried to say was that the odds were .5 to the 10th power that a sequence of ten heads in a row would occur, with no tails anywhere in the sequence. Just one tail starts the sequence again. This is not different than what was being said above and is also consistent with my reference to the article on the binomial distribution.



Anyone can try this. Toss a fair coin ten times. The odds are 999:1 against completing the sequence of ten identical results.

As soon as you get an opposite result, the string starts again and you have the same set of odds for the next string of ten identical results.



What exactly are we disagreeing about? ;-)



Best regards,



Steve




> Date: Sat, 20 Nov 2010 06:31:10 -0800
> From:
> To:
> Subject: Re: [DNA] Odds Are, It's Wrong - 5% of the time
>
> Hi Steven,
> Let us both read this web page carefully too so we understand what is
> happening because it is tricky:
> http://en.wikipedia.org/wiki/Gambler%27s_fallacy ...
> Al
>
> > On 11/19/2010 9:00 PM, Steven Bird wrote:
> > Read what I wrote, Al. Better yet, look here:
> >
> >
> > http://en.wikipedia.org/wiki/Binomial_distribution
> >
> >
> > Good night.
> >
> >
> >> Date: Fri, 19 Nov 2010 19:33:19 -0800
> >> From:
> >> To:
> >> Subject: Re: [DNA] Odds Are, It's Wrong - 5% of the time
> >>
> >> They are independent events, the odds are the same each time.
> >> Losing three times in a row has no bearing on what will happen on the
> >> next trial ...
>
>
> -------------------------------
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