Question: You ask your roommate to water a sickly plant while you are on vacation. Without water the plant will die with probability 0.8 and with water it will die with probability 0.1. With probability 0.85, your roommate will remember to water the plant.
(a) What is the probability that your plant is alive when you return? (You may use a tree diagram.)
(b) If the plant is alive when you return, what is the probability that your roommate remembered to water it?