A and B plays chess everyday . The probability that A beats B in any game is twice the probability that B beats A . The probability that B beats A is three times the probability that the game ends in a draw . What is the probability that the game ends in a draw ?

My working :

P(A wins ) = 2(1- P(A wins ))

P(A wins ) = 2/3

P(B wins) = 3(1-P(A wins)-P(B wins))

P(B wins) = 3(1-2/3-P(B wins ))

P(B wins )=1/4

P(draw)=1-2/3-1/4=1/12 --- my answer

My answer is wrong . I wonder where my mistake is .....