Question

if the odds against a certain event are 23 to 22, what is the probability of the event occuring? write your answer as a simplified fraction.

Explanation:

Step1: Recall odds - probability relationship

The odds against an event $E$ is given by $\frac{n(\text{not }E)}{n(E)}$. Here, odds against is $\frac{23}{22}$, so $n(\text{not }E)=23$ and $n(E) = 22$.

Step2: Calculate total number of outcomes

The total number of outcomes $n(S)=n(E)+n(\text{not }E)=22 + 23=45$.

Step3: Calculate probability of event

The probability of an event $E$ is $P(E)=\frac{n(E)}{n(S)}$. Substituting the values, we get $P(E)=\frac{22}{45}$.

Answer:

$\frac{22}{45}$