Question

Among 500 freshmen pursuing a business degree at a university, 319 are enrolled in an economics course, 240 are enrolled in a mathematics course, and 127 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

(a)
Let

A = Economics course

B = Mathematics course

Given:
P(A) = 319/500 =0.638

P(B) = 240/500 = 0.48

P(A and B) = 127/500 = 0.254

To find P(A and/or B):

By Addition Theorem:
P(A + B) = P(A) + P(B) - P(A and B)

              = 0.638 + 0.48 - 0.254 = 0.864

So,

P(Economics and/or Mathematics course) = 0.864

(b)

P(Exactly one of these two courses) = P(A + B)- P(A and B)

                                                       = 0.864 - 0.254 = 0.61

(c)

P(Neither A nor B) = 1 - P(A+B)

                          = 1 - 0.864 = 0.136