A planned community has 300 homes, each with an automatic garage door opener. The door opener has eight switches that a homeowner can set to 0 or 1. For example, a door opener code might be 01100101.

Question

Assuming all the homes in the community are sold, what is the probability that at least two homeowners will set their switches to the same code, and will therefore be able to open each other's garage doors?

Answer 1

100%