it is 2 to 1 = 2/3
odds against winning - as far as I know - on the basis of which I have been doing probability and getting answers means probability of losing
one can rephrase the question on this basis and start working. I am sure with this rephrasing one can get a solution. It may
not be a GMAT type, all the more it gives exposure to a tough problem. Anyway, one can ignore. But I am giving the solution here: -
There are two cases to consider:
(1) B rides, and (2) C rides.
(1) The probability that B rides is 2/3.
If B rides, the probabiity that A wins is 1/6. (Because, all the horses are equally likely to win)
Hence: P(B rides & A wins) = (2/3)(1/6) = 1/9
(2) The probability that C rides is 1/3.
If C rides, the probability that A wins is (3)(1/6) = 1/2.
Hence: P(C rides & A wins) = (1/3)(1/2) = 1/6.
Then: P(A wins) = 1/9 + 1/6 = 3/18 = 5/18 . . . and: P(A loses) = 13/18
The odds against his winning is 13 to 5