Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 62% of those who attended the meeting were stockholders and 47% were employees, what percent were stockholders who were not employees?

Solution:

Let U be the set of total people who attended the company meeting.

Let S and E represent the sets of people who were stockholders and employees of the company, respectively.

According to the question,

$n(U) = 100%$

$n(S) = 62%$

$n(E) = 47%$

$n(S \cup E)^c = 0$

To find: $n_o(S) = ?$

Using formulae,

$n(U) = n(S) + n(E) - n(S \cap E)$

$or, 100% = 62% + 47% - n(S \cap E)$

$or, 100% = 109% - n(S \cap E)$

$or, n(S \cap E) = 109% - 100%$

$\therefore n(S \cap E) = 9%$

And,

$n_o(S) = n(S) - n(S \cap E)$

$= 62% - 9%$

$= 53%$

Hence, the required percentage of stockholders who were not employees is 53%.

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