Problem 1. In an exam we have to speak about 1 topic out of 12 possible topics. There are 3 retake opportunity. We plan to apply one of the following two strategies. 1. strategy: For the first exam we learn perfectly 4 topics. If we fail, then for the second exam we learn another 4 topics (so at this moment we know 8 topics). Finally, if we fail, we learn all the 12 topics perfectly. 2. strategy: For the first exam we learn perfectly 6 topics. If we fail, then for the second exam we learn another 3 topics. Finally, if we fail, we learn all the 12 topics perfectly. In a given exam if we have to speak about a topic which we learned, we pass the exam, otherwise we fail. Which strategy should we choose if we would like to minimize the expected number of the exams.