At Northbend High School, 28% of students are Sophomores, 25% are Juniors, and 29% are Seniors. 17% of Sophomores, 26% of Juniors, and 60% of Seniors
drive to school. No freshmen drive to school.
Suppose we select one student from this school at random and record which class
they are in as well as whether they drive to school or not.
(a) Draw a tree diagram to model this random process.
(b) Find the probability that the student drives to school.
(c) What is the probability that he or she is a Senior given that the student drives
to school?
(d) Are the events "drive to school" and "junior" mutually exclusive? Explain!
(e) Are the events "drive to school" and "senior" independent? Justify your
answer.