A random question

Here's a random puzzler.

Ok I just decided on 2. I have the solution to the first one (amoeba)

1) Our friend, Mr. Amoeba has 3/4 chance of reproducing into 2 offsprings, who are exactly like him, or he'll just die. What is the chance that he'll live forever if the first offspring of each amoeba takes 1 month to reproduce(or die) while the second takes 2 months? (provided global warming doesn't kill him like 20 years later)

2) Oh noes! J------Y has taken Y--a-'s waterbottle again. And this just to happen in the infinite maze of RI (a prison containing many captives who are never able to escape the infinite labyrinth). The design of RI is really simple (except for the bit about infinite looping and alternate universes). It consists of 4 exits at each intersection (N,E,S,W), and all passageways are of equal lengths. Now, J------Y takes 2 seconds to run each passageway, and Y--a- only takes 1, and J------Y looks like he is in deep trouble now, but... aha! a catch. J------Y has managed to keep Y--a- preoccupied with a Maths problem for a whole 4 seconds! To make it worse, Y--a- has myopia and can only see 1 passageway away. J------Y and Y--a- cant stop running: one fears for getting caught, one fears for losing his waterbottle for all eternity. What are the chances that Y--a- can catch J------Y and reclaim his waterbottle? (well... eventually)