% 
% Written by:
% -- 
% John L. Weatherwax                2007-07-01
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

%format rat;

numOfTotalBalls = 10; 
numOfRedBalls   = 3; 
numOfBlackBalls = numOfTotalBalls-numOfRedBalls; 

cprod=1; adraw=1; 
while( numOfBlackBalls > 0 ) 
  % this is player A's chance to get red at this stage draw ...
  pADrawRed  = (numOfRedBalls/numOfTotalBalls);
  
  % this is player A's chance to get red at this depth in the tree ...
  p_i(adraw) = cprod*pADrawRed; 
  
  % to "keep going" A did not draw a RED ball
  cprod = (1-pADrawRed)*cprod;
  
  % update the ball count (A must not have drawn red):
  numOfBlackBalls=numOfBlackBalls-1;
  numOfTotalBalls=numOfTotalBalls-1; 
  
  % calcuate the probability that B draws red: 
  pBDrawRed = numOfRedBalls/numOfTotalBalls; 
  
  % to "keep going" B did not draw a RED ball
  cprod = (1-pBDrawRed)*cprod;
  
  % update the ball count (B must not have drawn red):
  numOfBlackBalls=numOfBlackBalls-1;
  numOfTotalBalls=numOfTotalBalls-1; 

  adraw = adraw+1; 
end

p_i 

sum( p_i )