In a demographic study, researchers gather data on the gender of children in families with more than two children. For each of the four possible outcomes $G G, G B, B G, B B$ of the first two children in the family, they find 50 families which started with that pair, and record the gender of the third child of the family. This produces the following table of counts:

First two children Third child $B$ Third child $G$

$\begin{array}{ccc}G G & 16 & 34 \\ G B & 28 & 22 \\ B G & 25 & 25 \\ B B & 31 & 19\end{array}$

In view of this, is the hypothesis that the gender of the third child is independent of the genders of the first two children rejected at the $5 \%$ level?

[Hint: the $95 \%$ point of a $\chi_{3}^{2}$ distribution is $7.8147$, and the $95 \%$ point of a $\chi_{4}^{2}$ distribution is $9.4877 .]$