 239
 14
 Problem Statement

One day the fox decided to hunt for rabbits. As he was very hungry, he made a plan: he'll go the a rabbit hole at a random time and will wait there for time ##t## (let's call this strategy ##A##) hoping that he'll encounter a rabbit. But that night he saw the devil in his dreams who said to him: "Fox! I know that a rabbit will show up at exaclty 11 o'clock." But the devil knew that the rabbit is very fast and it'll show up at time ##\epsilon## before 11. The next day the fox arrived at exactly 11 but he was late for the rabbit so he waited for time ##t## (let's call this strategy ##B##).
Which strategy is better for the fox?
In average two rabbits show up every 45 minutes and we say that strategy ##A## is better than strategy ##B## if it is true that with strategy ##A## the fox had a higher chance to catch at least one rabbit.
 Relevant Equations
 
So if 2 rabbits show up every 45 minutes then trivially one rabbit shows up every 22.5 minutes. With strategy ##A## the probability of catching a rabbit is ##\frac{t}{22.5}##. With strategy ##B## it is ##\frac{t}{22.5\epsilon}##, so strategy ##B## is always better. Am I correct or I'm missing something? This is posted as a harder problem in my assignements (however it turned ot with other problems that they're not that difficult either...).