Classic Probability Problems

Here are some classic probability problems. Please check back for updates on solutions for classic probability problems.

1. Birthday Problem
2. Buffon's Needle
3. Monty Hall
4. Leibniz’s mistake
5. The Three-Conered Duel
6. Gambler's Ruin
7. ...


Notes on Probability

Bayesian Updating with Discrete Priors:

Example 1. There are three types of coins which have different probabilities of landing heads when tossed. • Type A coins are fair, with probability 0.5 of heads • Type B coins are bent and have probability 0.6 of heads • Type C coins are bent and have probability 0.9 of heads Suppose I have a drawer containing 5 coins: 2 of type A, 2 of type B, and 1 of type C. I reach into the drawer and pick a coin at random. Without showing you the coin I flip it once and get heads. What is the probability it is type A? Type B? Type C?