aez-notes

Two urns contain red and black balls, all alike except for colour. Urn \(A\) has 2 reds and 1 black, and Urn \(B\) has 101 reds and 100 blacks. An urn is chosen at random, and you win a prize if you correctly name the urn on the bases of the evidence of two balls drawn from it. After the first ball is drawn and its colour reported, you can decide whether or not the ball shall be replaced before the second drawing. How do you order the second drawing, and how do you decide on the urn?

We want to minimise the entropy of the second draw to ensure that there is as much information in the second draw as possible. So, if you draw red first, replace it, and if you draw black first do not replace it. Following this policy it is mechanical to compute the most likely urn.