If a student attends every management science class, the probability of passing the course is 0.70; but if the student only attends randomly, then the probability of passing the course is 0.40. If a student fails, he or she can take a makeup exam where the probability of passing is 0.70 if the student has attended every class. This probability of passing the makeup exam drops to 0.20 if the student has attended at random. Passing the course is worth" 5 credits, whereas full time attendance "costs" 2.5 credits in terms of energy and time, whereas random attendance "costs" only 1 credit. Assume that all failing students take the make up exam and that the payoff for failing is equal to 0. a) Use a decision tree to decide which the best attendance pattern to adopt. Write down the expected value of the best decision in the tab below