Question

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?

Answer 1

Explanation:

To calculate the probability that a freshman selected at random from this group is enrolled in exactly one of the two courses (economics or mathematics), we can use the principle of inclusion-exclusion:

Let:

A = Number of freshmen enrolled in economics course

B = Number of freshmen enrolled in mathematics course

AB = Number of freshmen enrolled in both economics and mathematics courses

Total number of freshmen = 1000

Number of freshmen enrolled in exactly one of the two courses = (A - AB) + (B - AB)

Given:

A = 520

B = 490

AB = 290

Number of freshmen enrolled in exactly one course = (520 - 290) + (490 - 290) = 230 + 200 = 430

Probability = Number of freshmen enrolled in exactly one course / Total number of freshmen

Probability = 430 / 1000 = 0.43

So, the probability that a freshman selected at random from this group is enrolled in exactly one of the economics or mathematics courses is 0.43, which is equivalent to 43%.