In this exercise you are going to build a simple Bayes box to figure out the posterior probabilities for a simple experiment involving black balls and white balls to illustrate how adding information to a situation can change probabilities. This helps illustrate one of the main principles of Bayesian statistics. Imagine that your friend has a bowl and it is filled with black marbles and white marbles. She then takes out three marbles and puts them in a velvet bag. You do not know what the color of any marble is that she put in the bag. Follow the following steps to fill out the Bayes box. 1. In the hypotheses column list out all of the possible combinations for marble colors that might be in the bag. 2. What is the prior probability of each hypothesis being true given you know nothing about what the actual number of white balls and black balls that are in the velvet bag? Put this in the Prior Probaility column. Be sure to copy the information from step 1 above into this table as well. 3. Now imagine that you get to pull out one marble from