There are two more assignments in a class before its end, and if you get an A on at least one of them, you will get an A for the semester. Your subjective assessment of your performance is:

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Let’s develop a joint-probability table to analyze this problem (the letters a – h represent probability values. For example, a is the probability of getting an A on both the paper and the exam; b is the probability of getting an A on the exam, but not on the paper; while g is the sum of a and d, and represents the probability of getting an A on the paper).

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a. (2 pts.) What does c + f equal?

b. (2 pts.) What does a + b + d + e equal?

c. (4 pts.) What is the probability of getting an A on the exam?

d. (4 pts.) What is the probability of getting an A in the course?

e. (4 pts.) Are the grades on the assignments independent (explain your answer mathematically)?