In: Statistics and Probability
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.)
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: