MathDB

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 5K, what is the chance he still has it when he finished the 5K?
Proposed by Zack Lee, Daniel Li, Dilhan Salgado

Problem Statement