Exercise 1 (50 points} A plane crashed in one of three region. It had a 50% chance to crash in region 1, a 30% chance to crash in region 2 and a 20% chance to crash in region 3. Searches are conducted. If the planed crashed in region 1' and a search is conducted there, it has 60% chance to nd the plane. In region 2, it is a 70% chance and in region 3 it is 50%. 1. If a search is conducted in each region, what is the probability that the plane is found? 2. What is this probability if two searches are conducted in each region? 3. What if only one search is conducted in a region chosen at random? 4. Let us assume that only one search is conducted, that it is over region 1 and that it does not nd the plane, what are the probabilities that the plane is in region 1,2 and 3? 5. Let us assume that one search is conducted ouer every region and that the plane is found, what are the probabilitues that the plane was in region 1, 2 and 3