#### Answer

$\frac{113}{174}$

#### Work Step by Step

If A and B are not mutually exclusive events, then
P(A or B) = P(A)+P(B) - P(A and B)
E: has completed four years of high school only or is a man.
A: has completed four years of high school only
B: a man
P(A) = $\frac{56}{174}$
P(B) = $\frac{82}{174}$
P(A and B) = $\frac{25}{174}$
P(E) = $\frac{56}{174}$ + $\frac{82}{174}$ - $\frac{25}{174}$
=$\frac{56 + 82 - 25}{174}$ = $\frac{113}{174}$