% Mysterious Transfer
% Content of a box denoted as a pair [#Black balls,#White balls]
% Contents at start: first box [8,4], second [4,6], third [2,2]
% Problem: From 1st box a ball is randomly selected and transferred
% to the 2nd box, then from the 2nd box a ball is selected and transferred
% to the 3rd box. Then, from the 3rd box a ball is selected: Find an
% approximation to the probability that the ball from the 3rd box was black?
%
clear allc
close all
disp('Misterious Transfer')
lw = 2;
set(0, 'DefaultAxesFontSize', 16);
fs = 15;
msize = 10;
rand('twister',0)
%
M=100000; %# of experiments
nb=0; %# of black balls selected
%
content1=[8 4];
for i=1:M
first = randsample('BW',1, true, content1); %draw 1st
if (first =='B') content2 =[5 6];
else content2=[4 7];
end
second = randsample('BW',1, true, content2); %draw 2nd
if (second =='B') content3 =[3 2];
else content3=[2 3];
end
third = randsample('BW',1,true,content3); %draw 3rd
if (third == 'B') nb = nb+1;
end
end
disp(['The prob of ball from the 3rd box black ', num2str(nb/M,5)]);
%
% exact 0.4867
%