T5.12 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
Machines 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 with 30% for Machine B and 40% for Machine C. Suppose we
randomly select a part produced at the factory.
a. Find the probability that the part is defective.
b. If the part is inspected and found to be defective, what's the probability that
it was produced by Machine B?