The metropolitan school system consists of two districts, east and west. The east district contains 35% of all students, and the west district contains the other 65%. A vocational aptitude test was given to all students; 10% of the east district students failed, and 25% of the west district students failed. Given that a students failed, and 25% of the west district students failed. Given that a student failed the test, what is the posterior probability that the student came from east district?
- of students in east = 35%
- of students failing in east = 10%
- of students in west = 65%
This solution provides calculations for posterior probability.