Four sisters, one crazy trip, and one little hotel. Clara and her three sisters are going to Peru! Christina and Jen want to share a room (like they did as kids), while single girls Amy and Bridget like their privacy and each want their own room. We need to book a hotel in the Sacred Valley as we prepare to climb Machu Picchu. On any given night, the number of vacant rooms in the little hotel we've chosen has a Poisson distribution with = 5.

a. A Poisson distribution with = 5? What does that even mean?

b. What is the probability that the hotel has at least three vacant rooms on the night we need to stay?