Three machines A B and C are used to produce a large quantity of identical parts at a factory. Machine A produces 60% of the parts, while Machine B and C produce 30% and 10% of the parts, respectively. Historical records indicate that 10% of the parts produced by Machine A are defective, compared to 30% for Machine B and 40% for Machine C. Suppose we randomly select a part produced by one of these three machines at random.

If the part is inspected and found to be defective, what's the probability that it was produced by Machine C?