6. (5 marks) Suppose we are playing the 31-hat game, and the players with the red hats are precisely the odd primes, that is, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31. Is the state winning or losing? How does each player vote? Show your work!6. (5 marks) Suppose we are playing the 31-hat game, and the players with the red hats are precisely the odd primes, that is, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31. Is the state winning or losing? How does each player vote? Show your work