N2011 P2 Q9

Camera lenses are made by two companies, A and B. 60% of all lenses are made by A and the remaining 40% by B. 5% of the lenses made by A are faulty. 7% of the lenses made by B are faulty.

1. One lens is selected at random. Find the probability that
   1. it is faulty,[2]
   2. it was made by A, given that it is faulty.[1]
2. Two lenses are selected at random. Find the probability that
   1. exactly one of them is faulty,[2]
   2. both were made by A, given that exactly one is faulty.[3]