Question

if the probability of an event is $\frac{45}{52}$, what is the probability of the event not happening? write your answer as a simplified fraction.

Explanation:

Step1: Recall probability formula

The sum of the probability of an event $P(E)$ and the probability of its complement $P(\overline{E})$ is 1, i.e., $P(E)+P(\overline{E}) = 1$.

Step2: Solve for $P(\overline{E})$

Given $P(E)=\frac{45}{52}$, then $P(\overline{E})=1 - P(E)=1-\frac{45}{52}$.

Step3: Calculate the result

$1-\frac{45}{52}=\frac{52}{52}-\frac{45}{52}=\frac{52 - 45}{52}=\frac{7}{52}$

Answer:

$\frac{7}{52}$