Chances Are - Opinionator Blog - NYTimes.com

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?

….

Naturally, the first few semesters I taught this topic, I stuck to the book, inching along, playing it safe.  But gradually I began to notice something.  A few of my students would avoid using “Bayes’s theorem,” the labyrinthine formula I was teaching them.  Instead they would solve the problems by a much easier method.

What these resourceful students kept discovering, year after year, was a better way to think about conditional probability.  Their way comports with human intuition instead of confounding it.  The trick is to think in terms of “natural frequencies” — simple counts of events — rather than the more abstract notions of percentages, odds, or probabilities.  As soon as you make this mental shift, the fog lifts.

via Chances Are - Opinionator Blog - NYTimes.com.

A helpful way to think about a non-intuitive calculation.