Three machines A, B, and C are used to produce the same part, and their outputs are collected in a single bin. Machine A produced 26% of the parts in the bin, machine B 38%, and machine C the rest. Of the parts produced by machine A, 8% are defective. Similarly, 5% of the parts from B and 4% from C are defective. A part is picked at random from the bin.
a. If the part is defective, what is the probability it was produced by machine A?
b. If the part is good, what is the probability it was produced by machine B?