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