Question

Among 500 freshmen pursuing a business degree at a university, 323 are enrolled in an economics course, 205 are enrolled in a mathematics course, and 140 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.)

Answer 1

The probability of selecting a random student who is enrolled in both the courses  is 0.280.

Step-by-step explanation:

Here, the total number of freshman in the university = 500

The number of students enrolled in Economics = n(E)  = 323

The number of students enrolled in Mathematics = n(M)  = 205

The number of students enrolled in Both Economics and math

= n(E∩M )  = 140

Let F : Event of selecting a student who is enrolled in both the courses

So, from the given data:

$P(F) = \frac{\textrm{Total number of favorable outcomes}}{\textrm{Total number of outcomes}} \\= \frac{\textrm{Total number of students enrolled in BOTH courses}}{\textrm{Total number of students}} \\ = \frac{140}{500} = \frac{7}{25}$

So, the probability of selecting a random students who is enrolled in both the courses  is $(\frac{7}{25} ) = 0.280$