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    Using set theory to solve for the probability

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    A survey of a group of military personnel revealed the following information:
    95 officers
    90 minorities
    90 women
    40 women officers
    38 minority women
    40 minority officers
    23 women minority officers
    16 caucasian male enlisted personnel

    How many personnel were:
    a. interviewed
    b. enlisted minority women
    c. male minority officers
    d. enlisted
    e. officers, but not women or minority
    f. enlisted women
    g. minority women, but not officers

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    Solution Preview

    We use set theory to solve the problem.
    Suppose P is the set of all personnel interviewed. M is the set of all males. W is the set of all women. O is the set of all officers. N is the set of all minorities.
    From the condition, we have:
    95 officers, this means |O|=95
    90 minorities, this means |N|=90
    90 women, this means |W|=90
    40 women officers, this means |W and O|=40
    38 ...

    Solution Summary

    Set theory is used to solve for various probabilities. This is a well presented solution.