The probability of selecting one girl from the group is \(\dfrac n{16}\) where \(n\) is the number of girls in the group. Without replacing her, the probability of selecting another girl from the group would be \(\dfrac{n-1}{15}\). Assuming selection is independent, this means
\(\dfrac1{12}=\dfrac n{16}\times\dfrac{n-1}{15}\)
There are two solutions here, \(n=-4\) and \(n=5\). The number of girls in the group must be positive, so there must be 5 girls in the group.
