Stillwater Junior High divides students into teams taught by a group of teachers. The table shows the number of students in each team.
Team, Number of Students
Acers, 78
Blazers, 80
Outbacks, 83
Quasars, 77
Voyagers, 82
Total 400
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 a student from the Voyagers on the second try?
A. 81/399
B. 41/200
C. 1/82
D. 21/100
Since the probability of drawing any one student on the first try is the same for each student, the probability of drawing a student from the Voyagers on the first try is $\dfrac{82}{400} = \dfrac{41}{200}$.
If the first student drawn is from the Voyagers, there will be 81 students from the Voyagers left, and a total of 399 students left in the school. Therefore, the probability of drawing a student from the Voyagers on the second try is $\dfrac{81}{399}$.
Hence, the answer is $\boxed{\textbf{(A)}\ 81/399}$.
To find the probability of drawing a student from the Voyagers team on the second try, we need to determine the total number of students remaining in the school after the first draw and the number of students from the Voyagers team that could be drawn on the second try.
After the first draw, we know that one student from the Voyagers team has already been selected. So the total number of students remaining is 400 - 1 = 399.
Since the principal can draw the name of the same student twice, there is still a possibility that she could draw a student from the Voyagers team on the second try. The number of students from the Voyagers team that could be drawn on the second try is 82 (the initial number of students in the Voyagers team).
Therefore, the probability of drawing a student from the Voyagers team on the second try is 82/399.
So, the correct answer is option A: 81/399.