A metropolitan school system consists of three school districts-norths, south, central. The north district contains 25% of all students, the south district contains 40%, and the central district contains 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?
This solution contains a probability tree that helps calculate the joint probabilities and marginal probabilities of students going to North, South or Central. It also calculates the probability that a student selected at random failed the test. All steps are shown with clear explanations.