Question: The table below describes (approximately) the distribution of students by gender and college
at a mid-sized public university in the West.

College

Liberal Science

Education Engineering Arts & Math Agriculture Business Architecture

Male 200 3200 1500 1500 2100 1500 300

Female 300 1800 1500 1500 900 1500 200

If we were to randomly select one student from this university:

a. Find the probability that the selected student is a male.

b. Find the probability that the selected student is in the College of Liberal Arts.

c. Given that the selected student is female, what is the probability that she is enrolled in the College of Education?

d. Given that the selected student is enrolled in the College of Science & Math, what is the probability that the student is male?

e. Find the probability that the selected student is male and is enrolled College of Agriculture

f. Are the events the selected student is enrolled in the College of Architecture and the selected student is male independent events? Explain.