Kris is an enrolled student at the University of Sydney. Kris is 5 times more li
ID: 3237179 • Letter: K
Question
Kris is an enrolled student at the University of Sydney. Kris is 5 times more likely for a student in the Engineering and Information Technologies field than for those in other fields.
Use Bayes' rule to calculate an accurate subjective probability of your belief that Kris is in the faculty of Engineering and Information Technologies? Show your working in order to prove the result you obtained.
The table below shows the postgraduate and undergraduate student enrolments at the University of Sydney Total Faculty PG UG 141 Agriculture and Environment 516 657 Architecture, Design and Planning 708 682 1,390 7,054 Arts and Social Sciences 2,104 9,158 4,641 3,547 Business (Business School) 8,188 Dentistry 433 118 55 1,161 2,148 3,309 Education and Social Work Engineering and Information 4,423 1,624 6,047 Technologies Health Sciences 1,506 2,883 4,389 Law (Sydney Law School) 1,842 563 2,405 3,838 605 4,443 Sydney Medical School 1,732 Nursing and Midwifery 693 1,039 Pharmacy 421 1,069 1,490 6,786 1,167 5,619 Science Sydney College of the Arts 212 456 668 Sydney Conservatorium of Music 239 966 727 248 1,059 1,307 Veterinary Science Special University Programs 83 828 745 Total enrolments 21,061 33,253 54,314Explanation / Answer
Probability of being in Undergraduate or UG be P(UG). Therefore, P(UG) can be estimated to be:
P(UG) = 21061 / 54314 = 0.388
Similarly, probability of being in post graduate program,
P(PG) = 33203 / 54314 = 0.612
Probability that he is in Engineering and IT given he is a UG is
P(IT | UG) = 1624 / 21061 = 0.077
Probablity that he is in Engineering and IT given he is PG is
P( IT | PG) = 4423 / 33253 = 0.133
Probability that he is in IT or P(IT) can be obatined from Bayes' rule:
P(IT) = P(IT | UG) P(UG) + P(IT | PG) P(PG)
= 0.077 X 0.388 +0.133 X 0.612
= 0.1112
The accuate probability of Kris being in Faculty of Engineering and Information Technology as per the given data is only 0.1112
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.