function [] = chap_3_prob_29()
% 
% 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.
% 
%-----

% priors on the number of used balls selected: 
ubPriors = hygepdf( 0:3, 15, 6, 3 );

% the conditional probabilities: 
conditionals = [ nchoosek(9,0)*nchoosek(6,3), nchoosek(8,0)*nchoosek(7,3), nchoosek(7,0)*nchoosek(8,3), nchoosek(6,0)*nchoosek(9,3)]/nchoosek(15,3); 

% the result P(A): 
dot( ubPriors, conditionals )