Answer: Tuesday Teaser #10
The answer is surprisingly simple. If at any stage somebody sits in your seat (number 50), then you will inevitably be forced to sit elsewhere. Similarly, if at any stage somebody sits in seat number 1, then each subsequent person will have their seat available and so you will end up sitting in your own seat. Now at each stage, while seats 1 and 50 are free, there is an equal chance of a person choosing to sit in seat 1 as seat 50. Hence, your chance of sitting in your own seat is a half.
