This is a slight adaptation of a google interview question that I found entertaining.
You are given a jar with N coins, K of them are fair. The remaining coins have heads on both sides. You choose a coin at random from the jar and flip it m times.
If you get heads all m times, what is the probability that you selected a fair coin?
If m is 3, and N is 100, how many fair coins would need to be in the jar, for you to be at least 50% sure you selected a fair coin?