Tree diagrams for conditional probabilities

A course in statistics is one of the most difficult at the local university. Because of this, for the past decade the university has arranged for teaching assistants to hold frequent discussion sessions as part of the course. Since the inception of the discussion sessions, 60% of the students enrolled in the course regularly attended the sessions, and the other 40% did not. Students regularly attending the sessions have performed better than those not regularly attending. In particular, 70% of the students regularly attending the sessions received a grade of "B" or higher in the course, while only 40% of the students not regularly attending the sessions received a grade of "B" or higher in the course. Let D denote the event that a randomly chosen student (enrolled in the course} regularly attended the discussion sessions, and let D denote the event that a randomly chosen student did not regularly attend the discussion sessions. Let)? denote the event that a randomly chosen student received a grade of "B" or higher in the course, and let B denote the event that a randomly chosen student did not receive a grade of "B" or higher in the course. Fill in the probabilities to complete the tree diagram below, and then answer the question that follows. Do not round any of your responses. (If necessary, consult a list of formulas.) (a) Fill in the missing probabilities. P(B|D)=0.7 Pan= P(D)=D P(|D)=|] P(Dn B =|:| P(B|B)=0.4 P(B n B): I] P(B)=o4 P(B n E): U P(|3)=D (b) What is the probability that a randomly chosen student received a grade of "B" or higher in the course? I]