Many colleges require students to take a placement exam to determine which math courses they are eligible to take during the first semester of their freshman year. Of the 2938 freshmen at a local state college, 214 were required to take a remedial math course, 1465 could take a nonremedial, non–calculus-based math course, and 1259 could take a calculus-based math course. If one of these freshmen is selected at random, find the probability that this student could take
a. A calculus-based math course
b. A nonremedial, non–calculus-based math course
c. A remedial math course
Do these probabilities add up to 1.0? If so, why?