How many people are left?

I had time this evening to finally sit down and code up a simulator to answer the question I keep having when I watch this Last Man on Earth show (which I don't think is very good, since half the cast play horrible people, and because I can use the phrase "half the cast" on a show with that title).  Given that one person survived whatever killed everyone, how likely is it that there's another person alive as well.  This is basically a Bernoulli trial problem, where we don't know k or p.  I'm taking N = 300e6, which is close enough to the population of the US.  The results:

Normalized to the probability that everybody died, with the curves ranging for logarithmically spaced p values from 10**-8.4 to 10**-7.8.

If you think you're the only one alive, then you estimate that lp = -8.4.  However, once you find out that another person is alive, then lp >= -8.3 is the minimum (in this resolution), and those two cases have similar probabilities.  If you assume that k = 2 is the most likely probability, this moves lp to -8.1, and you have strong evidence that a third and fourth survivors are also likely.  Finding the third again bumps things up, and you can start expecting up to 8.  A fourth?  You've reached the other end of the simulation, and although the dynamic range of probability ratios increases, it's not excessive.

Basically, once the guy found Kristen Schaal, he's no longer the last man on Earth, and the likelihood of finding a lot more people jumps.  I will say that his strategy of travelling around writing the city he's living in seems like a good idea, assuming he wrote on a sign there that he's still driving around looking for people if they don't meet him.  That way, people will stay there and wait instead of assuming it's empty as well.  If he did meet a city with survivors, he could just change that sign to redirect to survivor-town.