Answer
The probability that a student is from a middle income or a high income family is $\frac{3}{5}$.
Work Step by Step
We know that the total number of students is 350.
Therefore, $ n\left( S \right)=350$
Also, the number of students from a middle income family is $160$.
Therefore, $ n\left( E \right)=160$
The probability of a student being from a middle income family is given below:
$\begin{align}
& P\left( \text{middle} \right)=\frac{\left( \begin{align}
& \text{Total number of students having } \\
& \text{ middle income parents} \\
\end{align} \right)}{\text{Total number of students}} \\
& =\frac{160}{350} \\
& =\frac{16}{35}
\end{align}$
Then, the number of students from a high income family is $50$.
The probability that a student is from a high income family is given below,
$\begin{align}
& \text{P}\left( \text{high} \right)=\frac{\left( \begin{align}
& \text{Total number of students having } \\
& \text{ high income parents} \\
\end{align} \right)}{\text{Total number of students}} \\
& =\frac{50}{350} \\
& =\frac{1}{7}
\end{align}$
Also, there is no common outcome. So,
$\begin{align}
& P\left( \text{A and B} \right)=P\left( A\cap B \right) \\
& =0
\end{align}$
If A and B are not mutually exclusive events, then
$ P\left( \text{A }or\text{ B} \right)=P\left( A \right)+P\left( B \right)-P\left( \text{A and B} \right)$
And the probability of the student being from a middle income or high income family is:
$\begin{align}
& P\left( \text{high or middle} \right)=P\left( \text{high} \right)+P\left( \text{middle} \right)-P\left( \text{high and middle} \right) \\
& =\frac{16}{35}+\frac{1}{7}-0 \\
& =\frac{21}{35} \\
& =\frac{3}{5}
\end{align}$
Thus, the probability that a student is from a middle income or a high income family is $\frac{3}{5}$.
