Problem:
Horses and are entered in a three-horse race in which ties are not possible. If the odds against winning are -to- and the odds against winning are -to-, what are the odds against winning? (By "odds against winning are to we mean that the probability of winning the race is .)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The probability that wins is and the probability that wins is . The sum of the winning probabilities for all three horses must be , so the probability that wins is . Hence the odds against winning are -to-.