By definition of independence, [tex]A[/tex] and [tex]B[/tex] are independent if [tex]P(A\cap B)=P(A)\cdot P(B)[/tex]. So neither the second nor third options can possibly be correct.
We have
[tex]P(A)\cdot P(B)=\dfrac35\cdot\dfrac23=\dfrac25[/tex]
[tex]P(A\cap B)=\dfrac15[/tex]
which are not equal, so no, [tex]A[/tex] and [tex]B[/tex] are not independent because the probabilities are not equal (last option).
