There are 1000 students in the senior class at a certain high school. The high school offers two Advanced Placement math / stat classes to seniors only: AP Calculus and AP Statistics. The roster of the Calculus class shows 100 people; the roster of the Statistics class shows 80 people. There are 45 overachieving seniors on both rosters.
What is the probability that a randomly selected senior is in at least one of the two classes ?
What is the probability that a randomly selected senior takes only one class?
Please show calculation.