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<<On Jul 12, 2010, at 12:01 AM, Néstor Gorojovsky wrote:
>
> Can anyone calculate the probabilities that Paul the octopus has
> reached his results by chance?
1/28 = . 0039
Statistically significant at the 99.6 % level.
Sheldrake strikes again!>>
Shane Mage >>
Since there is a disagreement between the number above and my number
below, I will demonstrate my reasoning.
Say the winner is always heads (H):
With 1 throw the possibilities are HT and TH or 1/2 probability =
2 to the first power
2
With 2 throws the possibilities are HH HT TH TT or 1/4
probability= 2 to the second power
4
With 3 throws the possibilities are HHH HTH HHT HTT
probablity 1/8 =
2 to the third power 8
TTT
THT TTH THH
With 4 throws the possibilities are HHHH HHHT HHTT HTTT
HTHH HTHT HTTH HHTH
Probability 1/16= 2
to the 4th power 16
TTTT
TTTH TTHH THHH
THTT
THTH THHT TTHT
Etc...Leading to the conclusion that the possibility of 9 straight
passes = 2 to 9th power = 512 with the chance of this happening 1/512
or 511 to 1.
From the internet note this on 7 throws:
<<With an "unbiased" coin your odds of a single toss are 1/2.
With two tosses, it becomes 1/2*2.
With 7 tosses, it is 1/2^7 (that 2 to the 7th power) = 1/128.
Not impossible, but it's a very low percentage (less than 1% of the tries).
Best regards,
Omnivorous-GA>> http://answers.google.com/answers/threadview/id/526284.html
7 throws ends with 128 different combinations and 128 is 2 to the 7th power.
Then there is this with 10 throws
<<0 heads: 1/1024 = 0.0009765625
1 head: 10/1024 = 0.009765625
2 heads: 45/1024 = 0.0439453125
3 heads: 120/1024 = 0.1171875
4 heads: 210/1024 = 0.205078125
5 heads: 252/1024 = 0.24609375
6 heads: 210/1024 = 0.205078125
7 heads: 120/1024 = 0.1171875
8 heads: 45/1024 = 0.0439453125
9 heads: 10/1024 = 0.009765625
10 heads: 1/1024 = 0.0009765625>>
http://mathforum.org/library/drmath/view/56660.html
The importance of this lies in the number "1024" which is 2 to the 10th power.
And 1/512 (which is 2 to the 9th power) = .002% even more impressive than the
comrade's assertion above
On 11:59 AM, johnaimani wrote:
> 2 to the 9th power or 511-1.
>
> Now 2 to the 9th is 512 but there is one chance that the octopus
> selects correctly.
>
>
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