Question

In a Derby race, the horse cusac's chance of winning is $\frac{1}{6}$, that of Lydo's winning is $\frac{1}{12}$ and of horse Delco's is $\frac{1}{8}$. If the race starts with 18 horses and only one horse wins, what is the probability that one of these 3 horses will win?

• A. $\frac{1}{8}$
• B. $\frac{3}{8}$
• C. $\frac{1}{4}$
• D. none

Answer 1

The correct option is B $\frac{3}{8}$

$Eachhorseisequalylikelytowinwithprobability=1/3Probabilitythathorsecusa{c}^{\prime }swintherace=\frac{1}{3}\ast \frac{1}{6}=\frac{1}{18}Probabilitythathorsecusa{c}^{\prime }swintherace=\frac{1}{3}\ast \frac{1}{12}=\frac{1}{36}Probabilitythathorsecusa{c}^{\prime }swintherace=\frac{1}{3}\ast \frac{1}{8}=\frac{1}{24}Probabilitythatoneamongthesethreehorseswintherace=\frac{1}{18}+\frac{1}{36}+\frac{1}{24}=\frac{3}{8}$