In a factory, machines \(A , B\) and \(C\) are all producing metal rods of the same length. Machine \(A\) produces \(35 \%\) of the rods, machine \(B\) produces \(25 \%\) and the rest are produced by machine \(C\). Of their production of rods, machines \(A , B\) and \(C\) produce \(3 \% , 6 \%\) and \(5 \%\) defective rods respectively.
Draw a tree diagram to represent this information.
Find the probability that a randomly selected rod is
produced by machine \(A\) and is defective,
is defective.
Given that a randomly selected rod is defective, find the probability that it was produced by machine \(C\).