Question: It was estimated that 30% of all seniors on a campus were seriously concerned about employment prospects, 25% were seriously concerned about grades, and 20% were seriously concerned about both.

(a) What is the probability that a randomly chosen senior form this campus is seriously concern about at least one of the two things?

(b) What is the probability that a student that is worried about grades is also worried about employment prospects?

If we define A = The student is concerned about employment prospects and
B = The student is concerned about grades;

(c) Are A and B mutually exclusive?

(d) Are A and B collectively exhaustive?