randomly choose an element from each row in a matrix if it was equal to one

i have the below matrix and i want to choose randomly one element from each row but only for the elements values equal to one and then save it in another matrix which will have the results (each row will have only one element equal to 1 ), anyone can help?

D=   1     1     0     1     1
     1     1     1     1     1
     0     0     0     0     0
     1     1     1     1     1
     1     0     1     0     1
     0     0     1     0     0
     0     0     0     0     0
     0     0     1     0     0
     0     0     0     0     0
     0     1     0     0     0

[Torsten]

And what if there is no 1 in the respective row ?

Answer 1

[Torsten]

You mean

D= [1     1     0     1     1
    1     1     1     1     1
    0     0     0     0     0
    1     1     1     1     1
    1     0     1     0     1
    0     0     1     0     0
    0     0     0     0     0
    0     0     1     0     0
    0     0     0     0     0
    0     1     0     0     0];
[N,M] = size(D);

DD = zeros(size(D));
for i = 1:N   
  idx = find(D(i,:)==1)
  n = numel(idx);
  if n ~= 0 
    in = randi(n);
    DD(i,idx(in)) = 1.0;
  end
end