In Steven Strogatz's New York Times blog opinionator.blogs. nytimes.com/2010/04/25/chances-are/?ref=opinion, the following problem was posed to highlight the confusing character of conditional probabilities.
Before going on vacation for a week, you ask your spacey friend to water your ailing plant. Without water, the plant has a 90 percent chance of dying. Even with proper watering, it has a 20 percent chance of dying. And the probability that your friend will forget to water it is 30 percent,
(a) What's the chance that your plant will survive the week?
(b) If it's dead when you return, what's the chance that your friend forgot to water it?
(c) If your friend forgot to water it, what's the chance it'll be dead when you return?
Solve parts (a), (b) and (c) of this problem.