I want to know if there's a method for determining the likelihood that a person is familiar with the most popular item in a set, given the number of items in said set they are familiar with. Here's the best example I can think of:
Andrew walks into a room with 20 dogs. He's played with 3 of these dogs, but we don't know which dogs in advance. More people have played with Spike than any other dog in the room. Let's say that Andrew's circle of friends is 10 people (including himself), and 5 of them have played with Spike. What are the odds that Andrew has played with Spike?
I'm sure there's an existing formula for this type of problem, but there are so many probability formulae that I can't find the one I need.