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Probability Tree
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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 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.

  1. Develop a probability tree showing all marginal, conditional, and joint probabilities.
  2. Develop a joint probability table.
  3. What is the probability that a student selected at random failed the test?
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