Some of the best math puzzles involve probability, mostly because they are counterintuitive in their answer until you see the solution. Take for example the Monty Hall problem. In that one, you are on a game show where you have three doors to pick from. Behind one there’s a car, behind the other two there are goats. You pick a door. The presenter opens one of the remaining doors and shows you the goat. You are then asked if you want to change your pick.
And while many people don’t like the idea, changing your pick is always the best option. With that in mind, let’s have a look at this intriguing little tease. University of Oxford undergrad Amie Campbell, assisted by Dr Tom Crawford, put together a little video on the Seat Reservation Probability Puzzle.
You have booked your favorite table in this restaurant out of the 100 available. The restaurant is completely full. Alas I.T. tragedy strikes. When the first patron arrives, the reservation software is not working and they are seated at a random table. Luckily, by the time the remaining guest arrives the system has been rebooted and they can be seated in their reserved table… unless someone else is already there. In that case, they will be placed in a random table.
You are the last guest to arrive because it is always good to be fashionably late. In this case, though, it means that getting your favorite table is out of your hands. Given all the possible positions of the other 99 guests, what is the probability you got the table you wanted?
My advice is to not overcomplicate it too much but if you want the solution check out the video below.