Splitting good and bad sweets between two boxes

You have $5$ good sweets and $5$ bad sweets and must distribute all of them between two boxes (each box gets at least one). Your brother, blindfolded, will choose a box at random and then a sweet at random from that box, and you get to keep it. If you arrange the sweets to maximise your chance of a good one, what is that chance?

$13/18$. Put a single good sweet alone in one box and the other nine sweets in the second box. Then the chance is $\tfrac12\cdot1+\tfrac12\cdot\tfrac49=\tfrac{13}{18}$, the best achievable.