Two people, let us call them A and B, decide to have a duel. They agree to meet at a designated spot sometime within the hour between noon to 1 PM. Each would arrive at a random time and stay for 5 minutes. If the other arrived within these 5 minutes, they would fight. Otherwise, they would leave, honor served. What is the probability that they will fight?
Solution: The figure below shows the possible arrival times of A and B on the two axes. It is clear that they will fight only of their arrival times are within the diagonal band in the figure. Hence the probability that they will fight is P = (602 – 552)/602 ~ 0.16. There is a 16 % chance of the duel taking place.
