If the probability of winning a race of an athlete is 1/6 less than twice the probability of losing the race,find the probability of winning the race

Let the probability of losing the race be x.
Therefore, the probability of winning the race = 2x - 1/6
BTP,
     2x - 1/6 + x = 1
or, 3x = 1 - 1/6
or, 3x = 5/6
or, x = 5/6 * 1/3
or, x = 5/18
Therefore, probabilty of losing the race = x = 5/18
                 probabilty of winning the race = 2x - 1/6 = 2 * 5/18 - 1/6 = 10/18 - 1/6 = 7/18
Ans: The probability of winning the race = 7/18