Answer
The probability that a randomly selected student attends a private college or is from a high-income family is $\frac{12}{35}$.
Work Step by Step
We know that the probability that a student attends a private college is:
$\begin{align}
& \text{P}\left( \text{private} \right)\text{ = }\frac{\text{students of private college}}{\text{total students}} \\
& =\frac{98}{350}
\end{align}$
And the probability that a student is from a high income family is:
$\begin{align}
& \text{P}\left( \text{high income} \right)\text{ = }\frac{\text{students from high income family}}{\text{total students}} \\
& =\frac{50}{350}
\end{align}$
And the probability that a student is from a high income family and attends private college is:
$\begin{align}
& \text{P}\left( \text{high income and private} \right)\text{ = }\frac{\text{students from high income family, attends private college}}{\text{total students}} \\
& =\frac{28}{350}
\end{align}$
Then, the probability that a student attends a private college or is from a high-income family is:
$\begin{align}
& \text{P}\left( \text{high income or private} \right)\text{ = P}\left( \text{private} \right)+\text{P}\left( \text{high income} \right)+\text{P}\left( \text{high income and private} \right) \\
& =\frac{98}{350}+\frac{50}{350}-\frac{28}{350} \\
& =\frac{98+50-28}{350} \\
& =\frac{120}{350}
\end{align}$
Solving further we get:
$\text{P}\left( \text{high income or private} \right)=\frac{12}{35}$
