function [] = chap_4_prob_46()
% 
% Written by:
% -- 
% John L. Weatherwax                2006-08-28
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----
  
%format rat; 

p_E_given_G = 0.;
for ii=9:12, 
    p_E_given_G = p_E_given_G + nchoosek(12,ii) * 0.8^ii * 0.2^(12-ii) ;
end

p_E_given_Gc = 1.;
for ii=9:12, 
    p_E_given_Gc = p_E_given_Gc - nchoosek(12,ii) * 0.1^ii * 0.9^(12-ii) ;
end

0.65 * p_E_given_G + 0.35 * p_E_given_Gc