A factory production line is manufacturing bolts using three machines, A, B and C. Of the total output, machine A is res

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A factory production line is manufacturing bolts using three
machines, A, B and C. Of the total output, machine A is responsible
for 20%, machine B for 35% and machine C for the rest. It is known
from previous experience with the machines that 5% of the output
from machine A is defective, 4% from machine B and 2% from machine
C. A bolt is chosen at random from the production line and found to
be defective. What is the probability that it came from machine A.
[Hints: let A, B, C and D be Machine A, B, C and Defective
respectively. Then, P(D)=P(D|A)*P(A)+P(D|B)*P(B)+P(D|C)*P(C )].