[tex]\frac{1}{6}[/tex]
1) Let's begin by finding the number of children: 50 girls and 35 boys=85 children.
2) The favorable event is 35 boys
3) So now, let's write out the following probability bearing in mind that one person was chosen right after the another.
[tex]P(boys\:and\:boys)=\frac{35}{85}\times\frac{34}{84}=\frac{1}{6}[/tex]