In the reality game show The Traitors there are $22$ participants.

Initially, $n$ participants are selected by the host Claudia Winkleman as

traitors.

The remaining "faithful" participants have to figure out who the

traitors are and banish them to win the game. Each night all

remaining participants, traitors and faithful, vote to banish someone

from the game. Whoever has the most votes is eliminated.

Subsequently, the traitors choose to "murder" one of the faithful

each night. In this manner, $2$ people are eliminated each night.

The game continues until there are only $2$ people left. If they are both

faithful, the faithful have won, otherwise the traitors have won.

Write a Monte Carlo simulation that calculates, given $n$ traitors, the

probability that the traitors will win.

Assume that the faithful are stupid and they always vote randomly.

Assume that the traitors select one of the faithful randomly, and all

of them vote for that same person. in java please