Box 1 contains 1000 Integrated Circuits of which 10% are counterfeit. Box 2 contains 2000 Integrated Circuits of which 5% are counterfeit. Externally, all IC's look identical. Two integrated circuits are picked from a (single) randomly selected box.
A. Find the probability that both integrated circuits are counterfeit.
B. Assuming that both integrated circuits are counterfeit, find the probability that they came from Box 1.