Question

Two athletes A and B participate in a race along with other athletes. If the chance of A winning the race is $\frac{1}{6}$ and that of B winning the same race is $\frac{1}{8}$, then the chance that neither A nor B wins the race, is

• A. $\frac{1}{4}$
• B. $\frac{7}{24}$
• C. $\frac{17}{24}$
• D. $\frac{35}{48}$

Answer 1

The correct option is C $\frac{17}{24}$

Chance of A winning the race =$\frac{1}{6}$and chance of B winning the race = $\frac{1}{8}$
$\therefore$ Chance of A or B wins the race =$\frac{1}{6}+\frac{1}{8}=\frac{14}{48}$
$=\frac{7}{24}$
Hence, chance that neither A nor B wins the race
$=1-\frac{7}{24}$
$=\frac{17}{24}$