Rug flaws on three square yards in exponential form

Flaws in Gabe's rugs occur as a Poisson process averaging $4$ per square yard. The chance that a $3$-square-yard sample has one or more flaws can be written as $1+\dfrac{a}{e^b}$. What is $a+b$?

$11$. The flaw count on $3$ square yards is Poisson with mean $12$, so $\mathbb{P}(\ge1)=1-e^{-12}$. That gives $a=-1$, $b=12$ and $a+b=11$.