A 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 student failed the test, what is the posterior probability that the student came from the east district?

Question

A 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 student failed the test, what is the posterior probability that the student
came from the east district?

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