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Using set theory to solve for the probability

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

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.