The odds are the ratio of an event occurring to that of its not occurring. The probability that the first slip drawn has a girl's name is 7/12. Having drawn a girl's name first, the probability of the second slip drawn having a girl's name is 6/11. Therefore $P(2\ girl's\ names)=\frac{7\times6}{12\times11}=\frac{7}{22}$ The probability of the first two slips not naming two girls is given by $P(other\ than\ 2\ girl's\ names)=1-P(2\ girl's\ names)=1-\frac{7}{22}=\frac{15}{22}$ Therefore the required odds are $\frac{7}{22}:\frac{15}{22}=7:15$