deletions | additions       diff --git a/p6.tex b/p6.tex  index 890c940..f6f2a0f 100644  --- a/p6.tex  +++ b/p6.tex 
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$P(\mbox{dot product}=1) = P(\mbox{only one 1 in n bits}) + P(\mbox{only 3 1s in n bits}) + P(\mbox{only 5 1s in n bits})...$  $P(\mbox{dot product}=1) = \sum_{i=0}^{n} {{n}\choose{2i+1}} * (\frac{1}{2})^n$ (\frac{1}{2})^n = (\frac{1}{2})^n * \sum_{i=0}^{n} {{n}\choose{2i+1}}$  Probability(dot product=1)=summation from (i=0,n) of nC(2i+1)*(1/2)^n   =(1/2)^n * summation from (i=0,n) of nC(2i+1)   This summation is just the sum of odd index binomial coefficients.  We know that the sum of the binomial coefficients from (0,n)=2^n