Q.If $P(A) = \dfrac{7}{13}$ for an event $A$, find $P(A')$.

[!TLDR] Apply $P(A')=1-P(A)$ with fractions sharing a common denominator. [!ANSWER] $P(A') = \tfrac{6}{13}$.

By the complement rule, $P(A') = 1 - P(A) = 1 - \dfrac{7}{13} = \dfrac{13}{13} - \dfrac{7}{13} = \dfrac{6}{13}$. As a check, $P(A)+P(A') = \dfrac{7}{13}+\dfrac{6}{13} = \dfrac{13}{13}=1$. [!ANSWER] $P(A') = \dfrac{6}{13}$.

Write $1$ as $\dfrac{13}{13}$ (matching the given fraction's denominator) before subtracting, to avoid decimal-conversion errors.

A common mistake is converting $7/13$ to a decimal, rounding it, and subtracting from $1$ — this loses precision; keep the calculation in exact fractions.