The probability of drawing a student from the Acers on the first try is 78/400 = 0.195.
Since the computer program allows for the same student to be drawn twice, there are still 77 students left in the Acers team after the first draw. Therefore, the probability of drawing a student from the Acers team on the second try, given that a student from the Acers team was drawn on the first try, is 77/400 = 0.1925.
Therefore, the probability she will draw the name of another student from the Acers on the second try is 19/100.
So, the correct answer choice is 19/100.