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. a. (5pts) Develop a probability tree showing all marginal, conditional, and joint probabilities. b. (5pts) Develop a joint probability table. c. (5pts) What is the probability that a student selected at random failed the test? d. (5pts) Given that a student failed the test, what is the posterior probability that the student came from the east district?

Answer 1

a)

let probability of east and west district are P(E) and P(W) ; also probabiltiy of passing and failing are P(P) and P(F)

b)

	fail	pass	total
east	0.035	0.315	0.35
west	0.1625	0.4875	0.65
total	0.1975	0.8025	1

c)

probability that a student selected at random failed the test =0.1975

d)

posterior probability that the student came from the east district given failed =0.035/0.1975=0.1772