A MathsJam Puzzle

This week was MathsJam week, and I really liked the puzzle that @KathrynHTaylor shared with us. I’ve reproduced it below: Can you do it and have you got an answer?

  • There are 50 seats on an aeroplane, and 50 people with numbered (in ascending order) tickets queing to board the plane. The first passenger doesn’t bother checking their seat number and sits randomly in a seat. The subsequent passengers sit in their allocated seated if it is free. If it has been taken, they then choose somewhere to sit (from the remaining free seats) at random. This process continues until all pasengers are seated. What is the probability that passenger 50 can sit in seat 50?

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