The principal uses a computer to randomly select the name of a student from all the students in the school. With the computer program, it is possible to draw the name of the same student twice. If the principal selects the name of a student from the Voyagers on the first try, what is the probability she will draw the name of another student from the Voyagers on the second try?
a. 1/78
b. 38/399
c. 19/100
d. 39/200
Let $n$ be the total number of students in the school, and let $v$ be the number of students in the Voyagers. If the principal selects a Voyager on the first try, then there are $v-1$ Voyagers left in the school out of $n-1$ total students. Therefore, the probability of selecting another Voyager on the second try is $\frac{v-1}{n-1}$.
Since there are no restrictions on $n$ or $v$ in the problem, we can choose convenient values to make the calculation easier. Let's say there are 100 students in the school, and 20 of them are Voyagers. If the principal selects a Voyager on the first try, then there are 19 Voyagers left out of 99 total students. Therefore, the probability of selecting another Voyager on the second try is $\frac{19}{99}=\frac{19}{100}$.
This matches answer choice $\boxed{\textbf{(c)}}$.