In my statistics class we just finished going over methods of simulating a study and we used one example that really caught my attention. The point of our simulation was to depict how a rumor/disease spreads throughout a population. We started with the entire class being uninformed and randomly selected one poor fool to start the rumor. Each turn, the people who knew get a chance to spread the information on the class by randomly choosing someone else to inform. If they target a clean person, the target starts spreading the rumor as well. If they target another person who knows the information (even themselves) both target and the person who picked the target get switched to a new state where they can't spread the rumor anymore but they can still stop other people from spreading by stopping people who tell them from telling any more. For clarification you cannot start spreading the instant you are infected, you must wait until the turn you were infected ends. As well, multpile people can target the same person randomly with no adverse effect.

I instantly set to work trying to mathematically describe the probability of each outcome, but after just creating a formula for some of the smaller cases my answers became quite daunting in size. On top of this I failed at discerning any pattern I could use to extend any formula out to generalize to all numbers. I might have just given up, but my teacher claims that in something he read a while ago he found a relatively simple equation to model this scenarios outcome. Anyone here think they can take a swing at finding this magic equation?

Just as a quick side note, I made a (not so small) java program to run a couple million simulations to see what happens and there seems to be some distribution such that the average amount of survivors is around one fourth the starting number and the most common result is slightly less than this mean value dropping off quicker with less survivors than more. If wanted I'll share the program so you can see the results for yourself.