Question: A metropolitan school system consists of three districts -north, south, and central. The north District contains 25% of all students, the south district contains 40%, and the central contains 35%. A minimum-competency test was given to all students; 10% of the north district students failed, 15%ofthe South students failed, and 5% of the central district students failed.

a) Develop a probability tree showing all marginal, conditional, and joint probabilities.

b) Develop a joint probability table

c) What is the probability that a student selected at random failed the test?