Suppose a large chat room for a country, what is the probability that two people know each other in real-life?
We have:
- n: The number of people in the chat room
- d: The number of persons the average person knows in real life
- P: The population of the country
I think the standard birthday problem would be
$$ 1 - \frac{(\frac{P}{d})!}{((\frac{P}{d})-n)!\ P^n} $$
but give the probability that two people have a common acquaintance, not that two people know each other.
How does one calculate the probability, that two people in the chat room know each other? Just multiplying the probability that the common acquaintance is in the room would neglect that one of the persons is the acquaintance themself.