Question

if the probability of an event not happening is $\frac{60}{97}$, what is the probability of the event happening? write your answer as a simplified fraction.

Explanation:

Step1: Recall probability formula

The sum of the probability of an event happening $P(E)$ and the probability of an event not - happening $P(\overline{E})$ is 1, i.e., $P(E)+P(\overline{E}) = 1$.

Step2: Solve for $P(E)$

We know that $P(\overline{E})=\frac{60}{97}$. So, $P(E)=1 - P(\overline{E})=1-\frac{60}{97}$.

Step3: Calculate the value of $P(E)$

$1-\frac{60}{97}=\frac{97}{97}-\frac{60}{97}=\frac{97 - 60}{97}=\frac{37}{97}$.

Answer:

$\frac{37}{97}$