Question

If the probability of winning a race of an athlete is $\frac{1}{6}$ less than twice the probability of losing, find the probability of losing the race.

• A. $\frac{7}{18}$
• B. $\frac{1}{3}$
• C. $\frac{3}{4}$
• D. $\frac{5}{6}$

Answer 1

The correct option is A $\frac{7}{18}$

Let, the probability of losing a race of athlete $=x$

Then, the probability of winning a race of athlete $=2x-\frac{1}{6}$

We know that the sum of probabilities of all possible outcomes of an event is 1.
(Note that the only possible outcomes of this event are winning the race and losing the race)
$\Rightarrow x+2x-\frac{1}{6}=1$
$\Rightarrow 3x=\frac{7}{6}$
$\Rightarrow x=\frac{7}{18}$

The probability of losing the race is $\frac{7}{18}$.