STOR-i blogs

A probability question that seems to be quite common in quant interviews is the airplane boarding problem. Imagine that there are $100$ people in a queue waiting to board a plane with $100$ seats numbered seats. The first passenger takes a random seat. Passenger $n>1$ will either take seat $n$ if it is not already taken or take a random available seat. What is the probability that the last passenger is seated? You are typically expected to answer such a question in $2$-$5$ minutes. Take some time if you want to try this problem on your own.  Passengers queueing to board a plane Without much thinking, many would expect the probability of such an event to be rather small. Perhaps in the order of $1/100$? In this problem intuition can be misleading. Let's consider simple cases. Instead of boarding $100$ people, consider $2$ instead. If there are $2$ seats, the probability that the second passenger takes the second seat is the probability that the first passenger...