#### Answer

The probability that a randomly picked American has done 4 years of high school only or is a man is $\frac{113}{174}$.

#### Work Step by Step

We know that the probability that a randomly picked American has done 4 years of high school only or is a man:
$\begin{align}
& P\left( \text{completed 4 years of high school} \right)=\frac{(\text{Numbers of students completed 4 years of high school)}}{(\text{Total numbers of students)}} \\
& =\frac{56}{174} \\
& P\left( \text{men} \right)=\frac{(\text{Total numbers of men)}}{(\text{Total numbers of students)}} \\
& =\frac{82}{174}
\end{align}$
$\begin{align}
& P\left( \text{4 years of high school only and a man} \right)=\frac{(\text{Total numbers men of high school only)}}{(\text{Total numbers of students)}} \\
& =\frac{25}{174}
\end{align}$
$\begin{align}
& P\left( \text{4 years of high school or is a man} \right)=\left[ P\left( \text{4 years of high school only} \right)+P\left( \text{man} \right)-P\left( \text{4 years of high school only and a man} \right) \right] \\
& =\frac{56}{\text{174}}+\frac{82}{\text{174}}-\frac{25}{174} \\
& =\frac{113}{174}
\end{align}$
Thus, the probability that a randomly picked American has done 4 years of high school only or is a man is $\frac{113}{174}$.