$4.$ A box contains a total of $100$ CDs that were manufactured on two machines. The following table gives the number of defective and good CDs manufactured on these two machines.

Defective Good Total

Machine A $105565$

Machine B $53035$

Total $1585100$

$($a$)$ If one CD is selected at random from the box, is that very high chance to select a good CD which is manufactured by machine A$?$ Explain. $(2$ m$)$

$($b$)$ Determine the probability that a randomly selected CD is either defective or it is not manufactured by machine B$.$ What is its relation with the probability of selecting a good CD which is manufactured by machine B$?(4$ m$)$

$($c$)$ Are the events $$defective$$ and $$manufactured by Machine B$$ independent? Justify your answer. $(3$ m$)$