Dilhan is running around a track for 12 laps. If halfway through a lap, Dilhan has his phone on him, he has a \frac{1}{3} chance to drop it there. If Dilhan runs past his phone on the ground, he will attempt to pick it up with a \frac{2}{3} chance of success, and won’t drop it for the rest of the lap. He starts with his phone at the start of the 5 \mathrm{K}, what is the chance he still has it when he finished the 5 \mathrm{K}?