Suppose I had two groups of people $A$ and $B$. I want to know the probability that the next person a randomly sampled person from group $A$ interacts with comes from group $B$.
Obviously the population distribution of group $A$ and $B$ matter, that is $P(A)$ and $P(B)$. But there are also population dynamics (say segregation or homophily) that increase the likelihood that people in group $A$ interact with people in group $A$ and people in group $B$ interact with people in group $B$.
What is the probability exactly one of the next five people a person from $A$ meets will be in group $B$? What is the probability it is exactly two people. Is there a distribution that describes this?