Problem
Suppose that a well-mixed urn contains 100 red and blue balls, in unknown proportion. Suppose you know that there are either 80 red balls or 20 red balls. You initially judge each of these possibilities to be equally likely and always update your probabilities via Conditionalization when learning propositional evidence. (Assume also that you respect the Principal Principle.)
A. If one ball is drawn at random and seen to be red, what is your new probability that the urn contains 80 red balls?
B. If 5 balls are drawn randomly (with replacement) and each is seen to be red, what is the new probability that the urn contains 80 red balls?
C. Now suppose you can tell the 5 balls drawn are all of the same color and that you think the color is probably red but (due to the lighting) can't be sure. Your probability that they are all red goes to 90% while the probability that they are all blue does to 10%. What is your new probability that urn contains 80 red balls?