## Human Error in the Urn Game

http://onlinelibrary.wiley.com/store/10.1093/ei/39.4.609/asset/ei%25252f39.4.609.pdf?v=1&t=i28bxn97&s=8225525c7a67bc97b8953718478c6da01bff8d5e

In class, one of the applications for Bayes’ Rule we discussed was to calculate probabilities in the urn game. That is, say we have an urn with red and blue marbles inside, two of one color and one of the other color, with a 1/2 chance of either color being the majority. If we draw a red marble, it is not very obvious what the probability is that the urn is majority red GIVEN that we drew a red marble. However, it is clear what the probability is that the urn is majority red (1/2), what the probability is that we draw a red marble given a majority red urn (2/3), and what the probability is of drawing  a red marble at all (1/2). Bayes’ rule gives us a relationship between these 4 probabilities, so that we can find the conditional probability we want in terms of the other 3 probabilities (2/3 in this case). This method extends to multiple rounds of the urn game, where players draw marbles in turn and announce their guess of what the majority color of the urn is, so that each player knows the guesses of all players that went prior (but not necessarily the actual color of their draw).