A large university has 12,600 male students. Of these students, 5312 are members of so-called
“Greek” social organizations (fraternities or sororities), 2844 are members of Greek service organizations, and the others are not members of either of these two types of Greek organizations. Similarly, the female students are members of Greek social organizations, Greek service organizations, or neither. Assuming that gender and membership are independent events, find the probabilities of the events in parts a to c:
a. A student is a member of a Greek social organization given that the student is a female.
b. A student is a member of a Greek service organization given that the student is a female.
c. A student is not a member of either of these two types of Greek organizations given that the student is a female.
d. If the university has 14,325 female students, is it possible that P (Greek social organization | male) = P (Greek social organization | female)? Explain why/why not.