Question

if the odds for a certain event are 21 to 5, what is the probability of the event occuring? write your answer as a simplified fraction.

Explanation:

Step1: Recall the formula for probability from odds

The odds in favor of an event $E$ is given as $a$ to $b$. The probability $P(E)$ is calculated as $P(E)=\frac{a}{a + b}$. Here $a = 21$ and $b=5$.

Step2: Calculate the probability

Substitute $a = 21$ and $b = 5$ into the formula $P(E)=\frac{a}{a + b}$. We get $P(E)=\frac{21}{21 + 5}=\frac{21}{26}$.

Answer:

$\frac{21}{26}$