Let <bblatex>C\sim Bernoulli(0.5)</bblatex>,
<bblatex>P(A=0,B=0|C=0)=P(A=1,B=1|C=0)=0.5</bblatex>,
<bblatex>P(A=1,B=0|C=1)=P(A=0,B=1|C=1)=0.5</bblatex>.
Then you can check that
<bblatex>P(A=0,B=0)=P(A=0,B=1)=P(A=1,B=0)=P(A=1,B=1)=0.25,</bblatex>
but
<bblatex> 0=P(A=0,B=1|C=0) < P(A=0|C=0)P(B=1|C=0)=0.5\times 0.5=0.25. </bblatex>
