Use overlap bounds before adding the conditional information

For events A and B, $P(A)=5/8$ and $P(B)=2/3$.

(i) Find the greatest and least possible values of $P(A\cap B)$.

It is given in addition that $P(A'\mid B')=3/8$.

(ii) Find $P(A'\cap B')$.

(iii) Find $P(A\cup B)$.

(iv) Determine if A and B are independent.

(v) Another event C satisfies $P(C)=3/8$, $P(A\cap C)=P(B\cap C)=1/4$ and $P(A\cup B\cup C)=11/12$. Find $P(A\cap B\cap C)$.