Use the following table to find the probability that a randomly chosen member of the Student Government Board is a senior or lives in off-campus housing. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
\begin{tabular}{|c|c|c|}
\hline \multicolumn{3}{|c|}{ Students on the Student Government Board } \\
\hline Classification & On-Campus Housing & Off-Campus Housing \\
\hline Freshman & 1 & 1 \\
\hline Sophomore & 2 & 2 \\
\hline Junior & 1 & 3 \\
\hline Senior & 4 & 2 \\
\hline Graduate Student & 1 & 2 \\
\hline
\end{tabular}

Step 1 ：First, we need to calculate the total number of students on the Student Government Board. This is done by adding up all the students in each category. We have 1 freshman living on-campus, 1 freshman living off-campus, 2 sophomores living on-campus, 2 sophomores living off-campus, 1 junior living on-campus, 3 juniors living off-campus, 4 seniors living on-campus, 2 seniors living off-campus, 1 graduate student living on-campus, and 2 graduate students living off-campus. This gives us a total of 19 students.

Step 2 ：Next, we need to calculate the number of seniors and the number of students living in off-campus housing. There are 4 seniors living on-campus and 2 seniors living off-campus, giving us a total of 6 seniors. There are 1 freshman, 2 sophomores, 3 juniors, 2 seniors, and 2 graduate students living off-campus, giving us a total of 10 students living off-campus.

Step 3 ：The probability that a randomly chosen member is a senior or lives in off-campus housing is the sum of the number of seniors and the number of students living in off-campus housing divided by the total number of students. However, since a student can be both a senior and live in off-campus housing, we are double counting those students. Therefore, we need to subtract the number of seniors living in off-campus housing from our numerator to avoid double counting. This gives us a probability of \(\frac{6 + 10 - 2}{19} = 0.7368421052631579\).

Step 4 ：Final Answer: The probability that a randomly chosen member of the Student Government Board is a senior or lives in off-campus housing is approximately \(\boxed{0.737}\).