Probability to win the $5000 found in the faculty lounge
What is the chance that each faculty member wins?
You and four colleagues find a $5000 bill on the floor of your department’s faculty lounge. You ask around but nobody seems to have any idea where it came from. None of you have change, so you agree to play a game of chance to decide who keeps it. The five of you sit around a table and the bill is placed in front of you as you are the most senior faculty member. The other faculty sit with the next senior person on your right then the next and so on. The game is played in turns. Each turn, the person in front of whom the bill is will throw a six-sided die. If any number from 1-4 shows up, (probability 2/3) the bill moves to the right one position (i.e. towards the next junior person). If 5 or 6 show up (probability 1/3) the bill stays put and the person who is sitting in front of the bill gets to keep it. The bill starts in front of you, and you get to throw first. What are the chances you win the money? And what are your colleagues’ chances in order of seniority to win the coin?
The solution can be found here.