A long time ago, a friend gave me a probability problem. Here is rough reconstruction.
A spaceship is lost in deep ($3$-d) space. Its home planet is $X$ meters away. Every second, the spaceship teleports $Y$ meters in a random direction. If it gets within $Z$ meters of its home planet, the spaceship stops teleporting and is rescued. Otherwise, it continues teleporting. The spaceship can only move through teleportation -- it begins stationary, and is stationary at each point it teleports to. What is the probability the spaceship makes it home safely?
I believe my friend told me this a classic problem from a well-known book. What is the exact citation?
My friend clearly had in mind problems E10.10 and problem E10.11 in Williams's Probability With Martingales.