You start with one robot. Each moment this robot can either self-destruct, do nothing, make one copy of itself, or make two copies of itself, each with equal probability. What is the probability that you eventually end up with no robots?

So there are 4 choices

1 destroys itself

1 does nothing

1 coppies itself

1 makes 2 coppies of itself

so 1 in 4 that is destroys itself in the first time

1 in 4 that is basically skips this turn

1 in 4 that is doubles itself

1 in 4 that you will have 3 robots

we can count the skip turn as nothing so

1 in 4 that is is destroyed

2 in 4 or 1/2 that is does not destory itself

so if it doubled itself, this makes it more complicated

if it tripples itself, this makes if even more complicate

not exactly sure what the correct answer is