Among 500 freshmen

Question

Among 500 freshmen pursuing a business degree at a university, 318 are enrolled in an economics course, 210 are enrolled in a mathematics course, and 120 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

Create a two way frequency chart using the info provided. Like this:

a) To find the probability of being enrolled in either, that would be 318 + 210 but since there are 120 in both, and you can't double count, subtract 120:

(318 + 210 - 120)/500 = 408/500 = 0.816

b) There are 198 that are "Econ Enrolled" AND "Not Math Enrolled". There are 90 that are "Math Enrolled" AND "Not Econ Enrolled". 198+90 = 288 and 288/500 = 0.576

c) There are 92 not enrolled in either so 92/500 = 0.184