In a soccer game (or football, depending on your country), there are 11 players on each team. Since there are 2 teams, there are 22 players in all, but the referee makes it 23 people on the pitch. Suppose there is a crime committed, and one of the people on the pitch has committed the crime. Each player is asked if they know who committed the crime. However, everyone on the first team says that someone on the second team did it, and everyone on the second team says that someone on the first team did it. So the referee gets the deciding vote. This clearly becomes unfair, because the referee will not pick himself, so each team manager gets a vote too. What is the probability that the managers both pick the referee, and the referee picks someone other than himself? Express your answer as a decimal to the nearest thousandth.
Details and Assumptions:
-The managers and referees both pick randomly, regardless of team .