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.

When answering the questions below, make sure to explain your answers (show how you got the answers). More than half of the points for each question are allocated to your explanations. Keep 4 digits after the period for all questions (e.g., 0.4500).

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? (4 points)

b.What is the probability that the student lives in the dormitories? (4 points) c.Given that a student does not live in the dormitories, what is the probability that she/he

is not from Tennessee? (4 points) d. Based on the information above, are "living in a dormitory" and "being from Tennessee"

independent events? Why? (3 points)