Among 500 freshmen pursuing a business degree at a university, 323 are enrolled in an economics course, 205 are enrolled in a mathematics co

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.)

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Ivy 1 week 2021-09-12T04:00:17+00:00 1 Answer 0

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    2021-09-12T04:01:26+00:00

    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

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