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Among 500 freshmen pursuing a business degree at a university, 311 are enrolled in an economics course, 243 are enrolled in a mathematics course, and 135 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?
a) an economics and/or a mathematics course.
b) exactly one of these two courses.
c) neither an economics course nor a mathematics course.

Sagot :

Solution :

Let A = Economics, B = Mathematics

n(A) = 311, n(B) = 243, [tex]$n(A \cap B) = 135$[/tex]

a). So, [tex]$n(A \cup B) = n(A) +n(B) - n(A \cap B)$[/tex]

                     = 311 + 243 - 135

                     = 419

b). n(A only) = 311 - 135

                   = 176

     n(B only) = 243 - 135

                   = 108

Exactly one of these two courses

  [tex]$=\frac{176+108}{500}$[/tex]

  = 0.568

c). Neither economics nor mathematics

    [tex]$=\frac{500-419}{500} $[/tex]

  [tex]$=\frac{81}{500}$[/tex]

 = 0.162

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