For a game, each of two people, A and B , has a bag containing three cards on which the numbers 1, 2, and 3 are written, each number on a different card. In the game, A and B each take out one card from their own bag and compare the numbers. If the numbers are the same, the game is a draw. If the numbers are different, the person with the greater number wins.
(1) For a single game the probability of a draw is $\frac { \mathbf { L } } { \mathbf { M } }$.
(2) If this game is successively played four times, replacing the cards after each game, let us find the probabilities for the following.
(i) The probability that A wins three times or more is $\frac { \mathbf { N } } { \mathbf{O} }$.
(ii) The probability that A wins once and loses once and two games are draws is $\frac { \mathrm { P } } { \mathrm { QR } }$.
(iii) The probability that the number of times that A wins and the number of times that B wins are the same is $\frac { \mathbf { S T } } { \mathbf { U V } }$. Hence, the probability that the number of times that A wins is greater than the number of times that B wins is $\frac { \mathbf { W } \mathbf { X } } { \mathbf{UV} }$.