Sixty percent of the student body at UTC is from the state of Tennessee (T), 30% percent are from other states (O), and the remainder are international students (I). Twenty percent of students from Tennessee live in the dormitories, whereas, 50% of students from other states live in the dormitories. Finally, 80% of the international students live in the dormitories.

Imagine we randomly pick a student from UTC.

a.What is the probability that the student lives in the dormitories and is from other states?

b.What is the probability that the student lives in the dormitories?

c.Given that a student does not live in the dormitories, what is the probability that she/he is not from Tennessee?

d. Based on the information above, are "living in a dormitory" and "being from Tennessee" independent events? Why?