belgian gangsters (probability)
Source: flanders '92
September 27, 2005
probability
Problem Statement
It has come to a policeman's ears that 5 gangsters (all of different height) are meeting, one of them is the clan leader, he's the tallest of the 5. He knows the members will leave the building one by one, with a 10-minute break between them, and too bad for him Belgium has not enough policemen to follow all gangsters, so he's on his own to spot the clanleader, and he can only follow one member.
So he decides to let go the first 2 people, and then follow the first one that is taller than those two. What's the chance he actually catches the clan leader like this?