5 To graduate from State University, Angie Warner needs to pass at least one of the three subjects she is taking this semester. She is now enrolled in French, German, and statistics. Angie’s busy schedule of extracurricular activities allows her to spend only 4 hours per week on studying.

Angie’s probability of passing each course depends on the number of hours she spends studying for the course (see Table 17). Use dynamic programming to determine how many hours per week Angie should spend studying each subject. (Hint: Explain why maximizing the probability of

passing at least one course is equivalent to minimizing the probability of failing all three courses.)

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TABLE 17 Hours of Study per Week 0 1234 Probability of Passing Course French German Statistics .20 .30 .35 .38 .40 33333 .25 .10 .30 .30 .33 .40 .35 .44 .38 .50