I have one bag containing 800 Skittles and 200 M&Ms, and another bag containing 800 M&Ms and 200 Skittles. I'm offering you your choice of bag, but you can only have one, and I might change my mind if you try to examine them too closely. Certainly you can't just look inside. Ridiculous. Unheard of. You like Skittles, and hate M&Ms. You pick a bag and start taking out pieces of candy from it (you put each piece back in the bag after noticing what kind of candy it is, because you like round numbers). In the first 5 pieces of candy you get, there are 4 Skittles and 1 M&M. Have you chosen the right bag? How sure are you of that? (70%? 80%? 98.5%?) Would you be more or less sure if you took out 4 more pieces of candy and got 2 of each type, for a total of 6 Skittles and 3 M&Ms? With applications ranging across robotics, medical diagnosis, the theoretical basis of science, and intelligent choice of bags of candy, Bayes' Theorem is a very simple and very useful piece of math that tells you how to make the most of the information you have.

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