Demonstrate the BinomialTheorem for the doggy problem.

The example is taken from:

Nahin, P. J., "Duelling Idiots and Other Probability Puzzlers,"
Princeton University Press.

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See also Plot2D, BinomialTheorem
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%   Copyright (c) 2003 Princeton Satellite Systems, Inc.
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births = [2 4 8 16 32 64 128];

pC = zeros(1,length(births));
for j = 1:length(births)
  pC(j) = BinomialTheorem( births(j), births(j)/2, 0.5 );
end

Plot2D( births, pC, 'Births', 'Probability', 'Probability of Half Male Half Female Births')
set( gca, 'xlim', [0 births(end)], 'xtick', births )


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