In an examination, the probability that a student will pass Mathematics is 0.8. If the student passes Mathematics, the probability that the student will pass Chemistry is 0.9. If the students fails Mathematics, the probability that the student will fails Chemistry is 0.4. 

(a) Calculate the probability that the student will pass i. Chemistry. ii. Mathematics given that the student passes Chemistry. 

(b) Find the probability that the student fail for both subjects, Mathematics and Chemistry. 

(c) Find the percentage that the student fails Mathematics in this examination. 

(d) State whether the events of a student who passes Mathematics and Chemistry are independent. Give reasons for your answer.