Question

if the odds for a certain event are 20 to 21, what is the probability of the event occuring? write your answer as a simplified fraction.

Explanation:

Step1: Recall the odds - probability formula

The odds in favor of an event $E$ is given by $\text{Odds}=\frac{\text{Number of favorable outcomes}}{\text{Number of non - favorable outcomes}}$. If the odds in favor of an event are $a$ to $b$, then the probability of the event $P(E)=\frac{a}{a + b}$. Here, $a = 20$ and $b=21$.

Step2: Calculate the probability

Substitute $a = 20$ and $b = 21$ into the formula $P(E)=\frac{a}{a + b}$. We get $P(E)=\frac{20}{20+21}$.
$P(E)=\frac{20}{41}$

Answer:

$\frac{20}{41}$