In my Random Walks class, I first learnt about this — there is always a first time you visit something and a last time, as being put together in the quote above. A bit philosophical way to start the conversation for a problem, but I hope you will find the statement relevant in your life as well as in this problem. For new readers, I have recently started a new series where I bring interesting probability puzzles and their solutions. You can also contribute your problems or solutions to this series, by reaching me out on LinkedIn, Twitter, Instagram or Email.
The problem goes like this…
A line of 100 airline passengers are waiting to board a plane. They each hold a ticket to one of the 100 seats on that flight. For convenience, let’s say that the n-th passenger in line has a ticket for the seat number n. Being drunk, the first person in line picks a random seat (equally likely for each seat). All of the other passengers are sober, and will go to their proper seats unless it is already occupied; In that case, they will randomly choose a free seat. You’re person number 100. What is the probability that you end up in your seat (i.e., seat #100) ?