There are $3 $ red pens and $4 $ blue pens in a box. Naeem randomly takes two pens from there and adds $2$ red pens. Now if Naeem's younger brother Arko comes and randomly picks a pen from there, the probability that he will pick a red pen is $\frac{p}{q}$ ( $p$ and $ q $ are relatively prime integers). Then what is the value of $p+q$?