Problem:
A metropolitan school system consists of three districts-north, south, and central. The north district contains 25% of all students, the south district contains 4O%, and the central district contains 35%. A minimum-competency test was given to all students; 10% of the north district students failed,5% of the south district students failed, and 5% of the central district students failed.
Required:
Question 1) Develop a probability tree showing all marginal, conditional, and joint probabilities.
Question 2) Develop a joint probability table.
Question 3) What is the probability that a student selected at random failed the test? Solve the given numerical problem and illustrate step by step calculation.