Among 500 freshmen pursuing a business degree at a university, 346 are enrolled

Question

Among 500 freshmen pursuing a business degree at a university, 346 are enrolled in an economics course, 237 are enrolled in a mathematics course, and 125 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

Let A be enrolling in economics course and B be enrolling in mathematics course.

n(U) = 500 n(A) = 346 n(B) = 237 n(A and B) = 125

(A) An economics and/or mathematics course

n(A or B) = n(A) + n(B) - n(A and B) = 346 + 237 - 125 = 458.

(b) Exactly one of these courses

n(A - B) + n (B - A) = n(A) + n(B) - n(A and B) = 346 + 237 - 2*125 = 333.

(c) Neither an economics course nor a mathematics course

n(A or B)' = n(U) - N(A or B) = 500 - 458 = 42.

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