Here's a question I was faced with recently:
I have an unbiased coin with one head side and one tail side, and a biased coin with two tail sides. I choose an coin whilst blindfolded, and flip the coin. The result is a tail. What is the chance that the coin is biased?
What is obvious is that I have a 50% chance of picking the biased coin to begin with, but what I am not sure about is whether or not the result of the flip affects the chance that I picked the biased coin.