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