1. The problem statement, all variables and given/known data In a high-school graduating class of 100 students, 54 studied math, 69 studied history, and 35 studied both math and history. If 1 of the students is selected at random, find the probability that (a) the student took math or history; (b) the student did not take either of these subjects; (c) the student took history but not math. 2. Relevant equations P = n/N 3. The attempt at a solution Ok. I am thinking that I actually need to figure out how many students took math only and history only (pretty sure this is just algebra). So I know that there are 54 math students; this must include those who studied both. Thus, the number of students who studied *math only* is 54 - 35 = 19. Similarly, those who took History only 69 - 35 = 34. So for (a) P(M U H) = (19 + 34) / 100 = 53/100 ... but this is wrong. Book says 22/25. So I am off to a bad start. What am I screwing up here?