What is the probability that a freshman selected at random from this freshman class is enrolled in each of the following?

Question

Among 500 freshmen pursuing a business degree at a university, 315 are enrolled in an economics course, 241 are enrolled in a mathematics course, and 148 are enrolled in both an economics and a mathematics course. What is the probability that a freshman selected at random from this group is enrolled in each of the following? (Enter your answers to three decimal places.)

(a) an economics and/or a mathematics course

 

(b) exactly one of these two courses

(c) neither an economics course nor a mathematics course

Answer 1

P(economics) = 315/500 = 0.63

P(mathematics) = 241/500 = 0.472

P(econ & math) = 148/500 =0.296

P(E or M) = P(E) + P(M) - PE and M) = 0.63 + 0.472 - 0.296 = 0.806

P(E and not M) or (M and not E)

P(E) - P(E and M) + P(M) - P(E and M)

0.63 - 0.296 + 0.472 - 0.296 = 0.51

P(not (E or M)) = 1 - P(E or M) = 1 - 0.806 = 0.194