## 43. The Big Race

In the big car race of the year, only cars of three brands participated: "Jaguar", "Ford", and "Maserati." If the odds against Ford losing are 2 to 2, and the odds against Jaguar losing are 5 to 1, then what should be the odds against Maserati losing?

(Note: "losing" here means "not winning," i.e., "not finishing in first place.")
43. The probability of "Ford" losing is $2 /(2+2)=$ $=1 / 2$. Therefore, the probability of "Ford" winning is also $1 / 2$. The probability of "Jaguar" losing is estimated at $5 /(5+1)=5 / 6$. Therefore, the probability of "Jaguar" winning is $1-5 / 6=1 / 6$.

![](https://cdn.mathpix.com/cropped/2024_05_21_fe999c0fe2ad81fc5164g-124.jpg?height=402&width=874&top_left_y=1261&top_left_x=588)

Thus, the probability of "Ford" or "Jaguar" winning is estimated by the number $1 / 2 + 1 / 6 = 4 / 6 = 2 / 3$, which is nothing other than the probability of "Maserati" losing. Therefore, one should bet 2 to 1 on "Maserati" losing.