Events A A\,A and B B\,B satisfy P(A)=516\displaystyle P(A)=\frac{5}{16}P(A)=165, P(B)=12\displaystyle P(B)=\frac12P(B)=21 and P(A∣B)=14\displaystyle P(A\mid B)=\frac14P(A∣B)=41.
Determine whether A A\,A and B B\,B are independent.