Question

If odds in favor of a target are 2:5, what is the probability of success?
 (A). $\dfrac{2}{5}$
 (B). $\dfrac{5}{2}$
(C). $\dfrac{2}{7}$
(D). $\dfrac{5}{7}$

Answer 1

Hint: As the ratio of odds in the favor of a target is given as 2:5 so we can write the odds in favor of target are 2x and odds not in favor of target are 5x. So, the total odds are $7x$. We know that: $\operatorname{P}\left( E \right)=\dfrac{\text{odds in favor}}{\text{total odds}}$where P(E) is the probability of success.

Complete step-by-step solution -
The ratio of odds in favor of the target is given as 2:5.
Now, from the ratio and proportion we can write:
Odds in favor of the target are equal to $2x$.
Odds against the target are equal to $5x$.
Therefore, the total odds are:
$5x+2x=7x$
Now, let us assume that the probability of success is equal to P (E).
Then writing probability of success in terms of odds in favor of target and the total odds we get,
$\operatorname{P}\left( E \right)=\dfrac{\text{odds in favor}}{\text{total odds}}$
Substituting $2x$ in place of odds in favor and $7x$ in place of total odds we get,
$\begin{align}
  & P\left( E \right)=\dfrac{2x}{7x} \\
 & \Rightarrow P\left( E \right)=\dfrac{2}{7} \\
\end{align}$
From the above solution, we have found the probability of success is $\dfrac{2}{7}$.
Hence, the correct option is (c).

Note: There is a possibility of misinterpreting the language of the question, i.e. you could have misunderstood the meaning of the language “odds in favor of a target are 2:5” as out of 5 odds, two are in favor of the target.
Actually, the language means that:
Odds in the favor of target and against the target are in the ratio of 2:5.