Question

An event has odds in favour $4:5$, then the probability that the event occurs, is
A. $\dfrac{1}{5}$
B. $\dfrac{4}{5}$
C. $\dfrac{4}{9}$
D. $\dfrac{5}{9}$

Answer 1

Hint: In this question, we are to find the probability of the event occurring. Here we have the odds of the event, we can calculate the probability.

Formula used: A probability is the ratio of favorable outcomes of an event to the total number of outcomes. So, the probability lies between 0 and 1.
The probability is calculated by,
\[P(E)=\dfrac{n(E)}{n(S)}\]
When two events happen independently, the occurrence of one is not impacted by the occurrence of the other.
For the events $A$ and $B$, $P(A\cap B)=P(A)\cdot P(B)$ if they are independent and $P(A\cap B)=\Phi $ if they are mutually exclusive.

Complete step by step solution: It is given that; an event has odds in favour of $4:5$.
So,
The number of favorable outcomes of the event to occur \[n(E)=4\]
The total number of outcomes
\[\begin{align}
  & n(S)=4+5 \\
 & \text{ }=9 \\
\end{align}\]
Then, the probability is
\[\begin{align}
  & P(E)=\dfrac{n(E)}{n(S)} \\
 & \text{ }=\dfrac{4}{9} \\
\end{align}\]

Thus, Option (C) is correct.

Note: Here we may go wrong with the odds ratio. Here the ratio is odds in favour of the event. So, we can find the required probability by using this ratio $P(E):\overline{P(E)}$. By substituting the appropriate values, the required probability is calculated. Here we may go wrong with the complimented probability.