Probability and Density?

I'm trying to determine the probability of meeting someone in a certain space. For example, randomly finding someone you know in a place this size with this many people this close together. I'm assuming that the relationship between density and probability is linear and that as density increases the probability of randomly finding someone you know increases. Are there any equations or formulas that relate probability and density so you can find out probability based on varying densities. I know that at its simplest the probability of finding someone you know in a population is just the number of people you know over the population, but is there anything that takes into account population density.

This sounds like an excellent application of random graph theory (each person is a random vertex, and each edge has a weight giving each path a weight as well). I read a few paragraphs on this a while back, but its been too long to fashion an application for you. I think you will be interested in it.
Check out Random Graphs, by Bollobas or The Strange Logic of Random Graphs, by Spencer.

This is a much more complicated problem than you seem to realize. You have to know about how people find each other. For example, can a person only see the nearest neighbors, or can he see a certain distance, which may mean seeing beyond the nearest neighbor? There are a lot of other details that I don't want to take the time to write about. I suggest you discuss this with another student in your class, the professor, or a grad student. You aren't going to find equations that model this situation. You would have to derive them yourself.

For clear idea about probability

http://www.futureaccountant.com