The probability is 1/11.
The probability that a girl is elected for one office is 4/12, since there are 4 girls out of 12 students.
The probability that a girl is elected for the second office is 3/11. This is because after one girl is elected, there are 3 girls left out of 11 students left.
Together, this gives us
4/12(3/11) = 12/132 = 1/11