Question 13
Horses $X,$ $Y,$ and $Z$ are entered in a three-horse race in which ties are not possible. If the odds against $X$ winning are $3$-to-$1$ and the odds against $Y$ winning are $2$-to-$3,$ what are the odds against $Z$ winning? (By “odds against $H$ winning are $p$-to-$q$” we mean that the probability of $H$ winning the race is $\frac{q}{p+q}.$)