Question

In a group of 16 students, the probability of randomly selecting 2 girls in a row without replacing the names back is 1/12. How many girls are in the group?

Answer 1

The probability of selecting one girl from the group is
`\frac 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
`(n-1)/(15)`. Assuming selection is independent, this means


`\frac1{12}=\frac n{16}*(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.