Question

In a horse race, the odds are $14: 1$ against the horse 'A' winning. In another horse race, the odds are 20:1 against the horse ' $B$ ' winning. The chance that none of the two horses win the race is

• A. $\frac{19}{21}$
• B. $\frac{8}{9}$
• C. $\frac{41}{45}$
• D. $\frac{31}{35}$

Answer 1

Answer: (D)

$P(A)=\frac{1}{15} ; P(B)=\frac{1}{21}$
$P ( A \text { or } B )=\frac{1}{15}+\frac{1}{21}=\frac{7+5}{105}=\frac{12}{105}=\frac{4}{35} $
$ P (\text { nobody wins })=1-\frac{4}{35}=\frac{31}{35}$