Suppose urn I has 2 blue and 8 gold balls, and urn II has 8 blue and 2 gold balls, and both Hilda and Phred agree on this. One of the two urns will be picked, with some unknown probability. You must say which urn was picked, and if you guess correctly you win $50, otherwise you win nothing. You can purchase one draw from the chosen urn for $1. (You will learn the color of the ball before you have say which urn was picked.) Suppose Hilda believes that urn I was chosen with probability 0.8, while Phred believes urn I was chosen with probability 0.2. Derive the optimal decisions (buying extra information, choosing an urn) for Hilda, Phred, and you under the assumption that you will combine Hilda's and Phred's assessments of their probabilities that urn I was chosen.