Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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

We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.