Among 500 freshmen pursuing a business degree at a university, 333 are enrolled

Question

Among 500 freshmen pursuing a business degree at a university, 333 are enrolled in an economics course, 210 are enrolled in a mathematics course, and 144 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

Explanation / Answer

We have n(economics) = 333 n(mathematics) = 210 n(economics and mathematics) = 144

(a) n(economics and/or mathematics) = n(economics) + n(mathematics) - n(economics and mathematics)

= 333 + 210 - 144

= 399.

(b) n(exactly one course) = n(economics) + n(mathematics) - 2 * n(economics and mathematics)

= 333 + 210 - 2*144

= 255.

(c) n(neither economics not mathematics) = n(freshmen) - n(economics and/or mathematics)

= 500 - 399

= 101.

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