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    Probability Tree

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    Problem 1:
    The Senate consists of 100 senators, of whom 34 are Republicans and 66 are Democrats. A bill to increase defense appropriations is before the Senate. Thirty-five percent of the Democrats and 70% of the Republicans favor the bill. The bill needs a simple majority to pass. Using a probability tree, determine the probability that the bill will pass.

    Problem 2:
    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.

    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?

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    Solution Summary

    This solution is comprised of detailed step-by-step calculation of the given problems in EXCEL and provides students with a clear perspective of the underlying concepts.