function [tE] = chap_7_prob_48()
% 
% Written by:
% -- 
% John L. Weatherwax                2007-04-02
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

%--
% this is for part (c) only
%--

% the "finite" expectation at the beginning
% -- from the first four rolls where we DON'T roll a five:
%
fe = 1*(1/5) + 2*( 4/5 )*(1/5) + 3*( (4/5)^2 )*(1/5) + 4*( (4/5)^3 )*(1/5); 

% the probability of not rolling a six in the first four rolls: 
% 
pA = (4/5)^4; 

% the "infinite" expectation in the tail:
%
tailE = 0; 
for kk=6:1000
  tailE = tailE + kk*( (5/6)^(kk-6) )*( 1/6 );
end
tailE = pA*tailE; 

% the total expectation: 
% 
tE = fe + tailE;