1. Suppose we have ten coins which are such that if the ith one is ?ipped then heads will appear with probability i/10, i = 1, 2, ... , 10. When one of the coins is randomly selected and ?ipped, it shows heads. What is the conditional probability that it was the ?fth coin?
2. Urn 1 has ?ve white and seven black balls. Urn 2 has three white and twelve black balls. We ?ip a fair coin. If the outcome is heads, then a ball from urn 1 is selected, while if the outcome is tails, then a ball from urn 2 is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails?