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