On a small island there are 25 inhabitants. One of these inhabitants, named Jack, starts a rumor which spreads around the isle. Any person who hears the rumor continues spreading it until he or she meets someone who has heard the story before. At that point, the person stops spreading it, since nobody likes to spread stale news.
a) Do you think all 25 inhabitants will eventually hear the rumor or will the rumor die out before that happens? Estimate the proportion of inhabitants who will hear the rumor.
How would one go about calculating the probability? I would try to block it out, but there are so many potential branches. This problem is in the simulations portion of our statistics book, but I'm curious if there is any other way that doesn't involve simulating the situation.