Impression Reach

Let’s say we have a very naive advertising platform. There is an audience of size A and a limited amount of impressions B.

Each of the impressions goes to just one user, defined at random. Every user in the audience has the same random chance of receiving each impression. 

1. Compute the probability that a user has exactly 0 impressions. 

2. What’s the probability that every person has at least 1 impression?