The following two-way table categorizes the class standing at Hope College for males and females in the fall of 2016. Let So 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 students. Find the probabilities described in (a)–(d). 

a. P(So) 

b. P(F) 

c. P(So|F) 

d. P(F|So) 

e. Are the events So and F independent? Why or why not?

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CLASS Freshmen Sophomore Junior Senior Non-degree Total Male Female Total 297 440 737 332 457 789 261 1445 709 325 545 49 68 1,267 1,955 870 117 3,222