Assignment:
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?
Provide complete and step by step solution for the question and show calculations and use formulas.