Based on a conversation from satyreyes comes a puzzle for which you might seek some medical attention:
Every day on a certain ward at Riddler Hospital, one patient is admitted who needs one day of treatment, one who needs two days and so on, up to seven days. Each patient remains in their own room for the duration of their stay.
You are a nurse who is assigned to a room at random on a particular day. What is the probability that the patient you see in that room will still be there tomorrow?
The probability the patient needs any of 1 to 7 days is $\dfrac{1}{7}$ .
The probability that today is not the last day for each of those is $\dfrac{n-1}{n}$.
$$ = \dfrac{617}{980} \approx 0.630$$