Question: Each morning, coffee is brewed in the school workroom by one of three faculty members, depending on who arrives first at work. Mr. Worcester arrives first 10% of the time, Dr. Currier arrives first 50% of the time, and Mr. Legacy arrives first on the remaining mornings. The probability that the coffee is strong when brewed by Dr. Currier is 0.1, while the corresponding probabilities when it is brewed by Mr. Legacy and Mr. Worcester are 0.2 and 0.3, respectively. Mr. Worcester likes strong coffee! \
(a) What is the probability that on a randomly selected morning the coffee will be strong? Show your work.
(b) If the coffee is strong on a randomly selected morning, what is the probability that it was brewed by Dr. Currier? Show your work.