Among 1,000 freshmen pursuing a business degree at a university, 520 are enrolled in an Economics course, 490 are enrolled in a Mathematics course, and 290 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 exactly one of these two courses?

Question

Quizplus · Accepted Answer

To find the probability that a student is enrolled in exactly one of the two courses, we need to subtract the number of students enrolled in both courses from the total number of students enrolled in either course.

Total enrolled in either Economics or Mathematics = 520 + 490 - 290 = 720

Probability of being enrolled in exactly one course = $\dfrac{	ext{enrolled in exactly one course}}{	ext{total enrolled in either course}}$

= $\dfrac{	ext{enrolled in Economics only + enrolled in Mathematics only}}{720}$

To find the number of students enrolled in Economics only, we subtract the number of students enrolled in both courses from the total number of students enrolled in Economics:

Enrolled in Economics only = 520 - 290 = 230

Similarly, the number of students enrolled in Mathematics only = 490 - 290 = 200

Therefore, the probability of a randomly selected student being enrolled in exactly one of these two courses is:

= $\dfrac{230 + 200}{720}$

= 0.430

= 43%

So, the answer is D.

Among 1,000 Freshmen Pursuing a Business Degree at a University