Question

Considered two events such that P(A)=3/5, P(B)=2/3, and P(AnB)=1/5. Are the events A and B independent events?

Yes, they are independent because P(A)xP(B)=P(AnB)

No, they are dependent because P(A)xP(B)=P(AnB)

Yes they are independent because P(A)xP(B)is not equal to P(AnB)

No they are dependent because P(A)xP(B)not equal to P(AnB)

Answer 1

By definition of independence, $A$ and $B$ are independent if $P(A\cap B)=P(A)\cdot P(B)$. So neither the second nor third options can possibly be correct.

We have

$P(A)\cdot P(B)=\dfrac35\cdot\dfrac23=\dfrac25$

$P(A\cap B)=\dfrac15$

which are not equal, so no, $A$ and $B$ are not independent because the probabilities are not equal (last option).