Posted by Sam on Wednesday, March 21, 2012 at 7:55pm.
This is a binomial expansion with p=0.522, and q=1-p=0.478.
We will calculate the terms of
(p+q)^26.
Using the notation
(n,r)=n!/((n-r)!r!)=n choose r
the binomial expansion can be expressed as
(p+q)^26
=p^26+(26,1)p^25q+(26,2)p^24q^2+...+(26,r)p^(26-r)q^r...+(26,1)pq^25+(26,0)q^26
P(12 tails)
=P(14 heads)
=(26,12)p^(12)q^(14)
=0.1285...
P(>22)
=P(23)+P(24)+P(25)+P(26)
=(26,3)p^23q^3+(26,2)p^24q^2+(26,1)p^25q+(26,0)p^26
=0.00001759...
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