I am looking for some help on understanding how to approach this problem / some intuition. It is a question from an old exam. I know the answer to (a) is 63%, and the answer to (b) is $\frac {0.21}{0.28}=0.75$. Its for an introductory statistics for economics course, and the only problems I seem to be struggling with are those involving probability.
Suppose that 30% of independent bookstores are profitable. There is a 70% probability that, if it is profitable, an independent bookstore will be taken over by a larger chain. Among non-profitable, independent bookstores only 10% are taken over.
(a) What is the probability that an independent bookstore is not profitable and not taken over? (b) If you observe a takeover, what is the probability that the store in question was profitable?