Question

At Case Western Reserve University, 46.6% of the student body are undergraduates and 53.4% of those enrolled are graduate students. 60.7% of undergraduate students participate in extracurricular activities, while only 32.1% of graduate students participate in extracurricular activities. A student who participates in extracurricular activities is randomly selected. What is the probability that the student is an undergraduate? Use Baye’s theorem to solve this problem. (Write your answer as a percent rounded to 1 decimal place.)

Answer 1

Solution:

Given: 46.6% of the student body are undergraduates and 53.4% of those enrolled are graduate students.

Let UG = Student is Undergraduates and G = Student is Graduates

Thus we have:

P(UG) = 0.466

P(G) =0.534

60.7% of undergraduate students participate in extracurricular activities.

Let EA = Students participate in Extracurricular Activities.

thus

P(EA | UG) = 0.607

32.1% of graduate students participate in extracurricular activities.

P(EA | G) = 0.321

We have to find:

P( the student is an undergraduate given that student participates in extracurricular activities ) =..........?

P(UG | EA) =..........?

Using Baye’s theorem of probability we get: