Let x be the probability of Janet   winning a hockey match;

    y be the probability of Chrissy winning a cricket match;

    z be the probability of Jack    winning a race.


From the problem, we have these equalities and inequalities

    x = ,               (1)

    z = 2y,                   (2)

     x <= 1, y <= 1, z<= 1.   (3)    <<<---===  general property of all probabilities . . . 


Hence,   <= 1,  which means  y <= .         (4)

Also    z = 2y <= 1,  which implies  y <= .        (5)


Comparing (4) and (5), we conclude that  y <= .


Due to (1), it implies then that  x <=  = .


It gives the final ANSWER :  the maximum probability of Janet winning the hockey match is  .