The following two-way table categorizes the class standing at Hope College for males and females in the fall of 2016. Let S represent the event a student chosen is a sophomore and let F represent the event the student chosen is a female. Suppose a student is chosen at random from all Hope College students. Find the following probabilities. 

a. P(F) 

b. P(S) 

c. P(S ∩ F) 

d. P(S ∪ F) 

e. Find P(S^c ∩ F^c) and describe what this probability is measuring (not what it does not measure). 

f. Find P(S ∪ Fc ) and describe what this probability is measuring (not what it does not measure).

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CLASS Male Female Total Freshmen 297 440 737 Sophomore 332 457 789 Junior 264 709 Senior 325 870 Non-degree 49 117 Total 1,267 3,222 445 545 68 1,955