Exercise 3 (30 points) We have three urns such that: 1. Urn 1 has 5 white balls and 4 black balls 2. Urn 2 has 2 white balls and 3 black balls 3. urn 3 has 6 white balls and 6 black balls 1. We select an urn at random and we then draw 2 balls from this urn (with- out replacing them). What is the probability to get two balls of the same color? Given that we drew two balls of the same color, what are the prob- abilities we selected urn 1, 2 and 3? 2. We select an urn at random and then draw one ball from each of the two other urns. What is the probability to get two balls of the same color? Given that we drew two balls of the same color, what are the probabilities we selected urn 1, 2 and 3? 3. We select an urn and draw a first ball that we then replace it in the urn, if it is black we draw a second ball from the same urn and if it is white we select at random one of the the two other urns and we draw a second ball from this urn. What is the probability that the second ball is black