[MrRubix]

Here's a hard one I doubt anyone here will get -- from one of my homeworks:

You have a system of N components. Each component will function, independently, with probability p. The total system of components will work if at least half of them are functioning. For what value of p is a 5-component system more likely to operate than a 3-component system? How about a (2k+1) component system over a (2k-1) component system?