# 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

https://brainmass.com/math/probability/using-set-theory-solve-probability-4165

#### 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.