Question

If the odds in favor of an event be $3:5$, then the probability of non-occurrence of the event is
$1)\text{ }3/5$
$2)\text{ 5}/3$
$3)\text{ }3/8$
$4)\text{ 5}/8$

Answer 1

Hint: In this question we have been given the odds in favor of an event. Given the data, we have to find the probability of non-occurrence of the event. We will solve this question by first finding the number of outcomes in favor of the event and the number of outcomes against the event. We will then find the total number of outcomes based on the sum of the both and find the probability of non-occurrence to get the required solution.

Complete step by step answer:
We have the odds in the favor of the event given to us as:
$\Rightarrow 3:5$
Therefore, we can say that the number of outcomes in favor of the event are $3$ and the number of outcomes against the event are $5$.
Therefore, the total number of outcomes will be the sum of both, mathematically, we can write:
$\Rightarrow 3+5$
On adding, we get:
$\Rightarrow 8$
Now the probability of non-occurrence will be the number of outcomes against the event divided by the total number of outcomes.
Mathematically, we can write:
$\Rightarrow P\left( {\bar{E}} \right)=\dfrac{3}{8}$, which is the required solution.

So, the correct answer is “Option 3”.

Note: In these types of questions both the parts of the ratio should be added to find the total number of outcomes. It is to be remembered that the probability of an event is between $0$ and $1$. Probability can never be negative. It is to be remembered that $P\left( E \right)=1-P\left( {\bar{E}} \right)$, where $P\left( E \right)$ is the probability of occurrence and $P\left( {\bar{E}} \right)$ is the probability of non-occurrence.