smc

Let the probability that a boy is chosen be $p$, so the probability that a girl is chosen is $1-p$ (as the probabilities must sum to $1$). Therefore $$\begin{array}{rl}\frac{2}{3}(1-p)=p& ⟺2(1-p)=3p\\ & ⟺2-2p=3p\\ & ⟺5p=2\\ & ⟺p=\frac{2}{5}.\end{array}$$ Now simply notice that the probability a boy is chosen is precisely the proportion of the number of boys out of the total number of students (boys and girls), so the answer is precisely $\boxed{\frac{2}{5}}$.