Imagine that a small hospital’s emergency room has an average of 20 admissions per Saturday night. If you were a doctor working overtime on such a Saturday night, you might want to know the probability of having a quiet night, one that would let you catch up on some much-needed sleep. Let’s call a quiet night one in which five or fewer admissions take place. What is the chance that you get some sleep? Assume that admissions are independent of one another and are just as likely to land in one instant in time as another on a Saturday night.