19. In a major state university, to study the performance relationship between calculus I and calculus II grades, the mathematics department reviewed the letter grades of all students who had taken both of the calculus courses in the last twenty years. For each pair of letter grades (X, Y ), the department calculated the proportion of all of the students who had earned X in calculus I and Y in calculus II. The results are given in the following table.

According to the rules of this university, if a student takes a course several times, only the last grade will be recorded. Based on this table, find the probability that a randomly selected student

(a) does better in calculus I than in calculus II;

(b) does better in calculus II than in calculus I;

(c) earns the same letter grade in both calculus courses.

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Calculus I F Calculus II FDC BA EDCBA F 0.00 0.00 0.00 0.00 0.00 0.08 0.05 0.04 0.02 0.01 0.02 0.03 0.18 0.08 0.02 0.01 0.01 0.09 0.07 0.04 0.00 0.01 0.06 0.10 0.08