2. A facory has two machines A and B. past records shows that machine A produces 30% of the total output and Machine B the remaining 70%. machine
A produces 5% defective articles and machine B produces 1 % defective
items. An item is drawn at random and found to be defective. What is the
probability that it was produces a) by machine A b) by machine B?

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?